%A Robert Vanderbei %A Hande Yurttan Benson %T On Formulating Semidefinite Programming Problems as Smooth Convex Nonlinear Optimization Problems %D January 4, 2000 %Z Wed, 2 Feb 2000 23:00:00 GMT %I DIMACS %R 2000-01 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-01.ps.gz %X

Consider the diagonal entries d_j, j=1,2,...,n, of the matrix D in an LDL^T factorization of an n-by-n matrix X. As a function of X, each d_j is well-defined on the closed domain of positive semidefinite matrices. We show that these functions are twice continuously differentiable and concave throughout the interior of this domain. Using these facts, we show how to formulate semidefinite programming problems as standard convex optimization problems that can be solved using an interior-point method for nonlinear programming.

Note: This research has been facilitated by the Special Year on Large Scale Discrete Optimization, via a graduate fellowship and the Workshop on Semidefinite Programming and Its Applications to Large Scale Optimization.

%A Yuval Shavitt %A Peter Winkler %A Avishai Wool %T On the Economics of Multicasting %D January 13, 2000 %Z Wed, 2 Feb 2000 23:00:00 GMT %I DIMACS %R 2000-02 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-02.ps.gz %X

A supplier of multicast information services will often be faced with the following problem: Broadcasting to the whole customer base (including non-paying customers) is cheaper than multicasting only to the paying customers. However, broadcasting discourages potential customers from paying. The result is an economic game in which the supplier tries to maximize profit in the face of rational, but not omniscient, behavior by customers.

In this work we build a model for such environments, which we believe is both reasonably realistic and amenable to mathematical analysis. The supplier's basic strategy is to broadcast every service for which the fraction of subscribed customers exceeds some threshold. We then model the customers' behavior, taking into account the possibility of customers receiving services for free. From this model, coupled with some mild assumptions on the supplier's cost structure, we can find the optimal setting of the supplier's broadcast threshold. The solution necessarily depends on choosing functions which describe the customers' utility for the offered services; we study in detail several such choices.

In all the examples we studied, our model predicts that the supplier's profits will be maximized if the supplier's broadcast threshold is set below 100%: The loss in revenue due to customers subscribing to fewer services is offset by the cost savings made possible by broadcasting the most popular services to all customers. We found our model to be fairly robust with respect to parameter choices. As such, we believe it can be of value to a supplier in devising a multicast/broadcast strategy, and that broadcasting when subscriptions are sufficiently high is likely to be the approach of choice in maximizing profits.

%A Alexander Kelmans %A Igor Pak %A Alexander Postnikov %T Tree and Forest Volumes of Graphs %D January 27, 2000 %Z Wed, 2 Feb 2000 23:00:00 GMT %I DIMACS %R 2000-03 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-03.ps.gz %X

The tree volume of a weighted graph $G$ is the ``sum'' of the tree volumes of all spanning trees of $G$, and the tree volume of a weighted tree $T$ is the product of the edge weights of $T$ times the ``product'' of the letters of the Pr\"{u}fer code of $T$ where the vertices of $G$ are viewed as independent indeterminants that can be multiplied and commute. The forest volume of $G$ is the tree volume of the graph $G^c$ obtained from $G$ by adding a new vertex $c$ and connecting every vertex of $G$ with $c$ by an arc of weight 1. We show that the forest volume is a natural generalization of the Laplacian polynomial of graphs and that it also can be expressed as the characteristic polynomial of a certain matrix similar to the Laplacian matrix. It turns out that the forest volumes of graphs possesses many important properties of the Laplacian polynomials, for example, the reciprocity theorem holds also for the forest volumes. We describe two constructions of graph compositions, and show that the forest volume of a composition can be easily found if the ``structure'' of the composition and the forest volumes of the graph--bricks are known. As an illustration of the results on the forest volume of graph--compositions we give a combinatorial interpretation and proof of Hurwitz's identity.

Keywords: graph, tree, forest spanning tree, Laplacian matrix and polynomial, tree and forest volume.

%A M. Bramson %A J. L. Lebowitz %T Spatial Structure in Low Dimensions for %D March 13, 2000 %Z Wed, 19 Apr 2000 16:00:00 GMT %I DIMACS %R 2000-04 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-04.ps.gz %X Consider the system of particles on ${\Bbb Z}^d$ where particles are of two types, $A$ and $B$, and execute simple random walks in continuous time. Particles do not interact with their own type, but when a type $A$ particle meets a type $B$ particle, both disappear. Initially, particles are assumed to be distributed according to homogeneous Poisson random fields, with equal intensities for the two types. This system serves as a model for the chemical reaction $A+B\to inert$. In [BrLe91a], the densities of the two types of particles were shown to decay asymptotically like $1/t^{d/4}$ for $d<4$ and $1/t$ for $d\geq 4$, as $t\to\infty$. This change in behavior from low to high dimensions corresponds to a change in spatial structure. In $d<4$, particle types segregate, with only one type present locally. After suitable rescaling, the process converges to a limit, with density given by a Gaussian process. In $d>4$, both particle types are, at large times, present locally in concentrations not depending on the type, location or realization. In $d=4$, both particle types are present locally, but with varying concentrations. Here, we analyze this behavior in $d<4$; the behavior for $d\geq 4$ will be handled in a future work [BrLe99]. %A R. Esposito %A J. L. Lebowitz %A R. Marra %T On the Derivation of Hydrodynamics from the Boltzmann Equation %D March 13, 2000 %Z Wed, 19 Apr 2000 16:00:00 GMT %I DIMACS %R 2000-05 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-05.ps.gz %X We review the main ideas on the derivation of hydrodynamical equations from microscopic models. The Boltzmann equation, which is a good approximation for the evolution of rare gases, provides an useful tool to test these ideas in mathematically controllable situations such as the Euler and incompressible Navier-Stokes limits, which we describe in some detail. We also discuss the heuristics and some few rigorous results available for stochastic particle systems. %A Lance Fortnow %A Dieter van Melkebeek %T Time-Space Tradeoffs for Nondeterministic Computation %D March 13, 2000 %Z Wed, 19 Apr 2000 16:00:00 GMT %I DIMACS %R 2000-06 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-06.ps.gz %X

We show new lower bounds for satisfiability and nondeterministic linear time. Satisfiability cannot be solved on general purpose random-access Turing machines in time n1.618 and space no(1). This improves recent results of Fortnow and of Lipton and Viglas.

In general, for any constant a less than the golden ratio, we prove that satisfiability cannot be solved in time na and space nb for some positive constant b. Our techniques allow us to establish this result for b < ((a+2)/a2-a)/2. We can do better for a close to the golden ratio, for example, satisfiability cannot be solved by a random-access Turing machine using n1.46 time and n.11 space. We also show the first nontrivial lower bounds on machines using sublinear space. For example, there exists a language computable in nondeterministic linear time and n.619 space that cannot be computed in deterministic n1.618 time and no(1) space.

Higher up the polynomial-time hierarchy we can get better bounds. We show that linear-time alternating computations with a most k alternations require essentially nk time if we only allow no(1) space. We also show new lower bounds on conondeterministic versus nondeterministic computation.

%A Italo J. Dejter %A Oriol Serra %T Efficient Dominating Sets in Cayley Graphs %D March 16, 2000 %Z Wed, 19 Apr 2000 16:00:00 GMT %I DIMACS %R 2000-07 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-07.ps.gz %X

An independent set $C$ of vertices in a graph is an efficient dominating set when each vertex not in $C$ is adjacent to exactly one vertex in $C$.

A countable family of nested graphs, each of which has at least one efficient dominating set, is produced for each real number in the unit interval [0,1].

These families range from star graphs, for which the efficient domination property was proved by Arumugam and Kala, to pancake graphs.

The families obtained are extended to partitions of the vertex sets into efficient dominating sets. Uniqueness holds for the given partitions whenever the countable family is not that of the star graphs.

For star graphs, all the possible ways in which such a partition occurs are established.

%A Peter C. Fishburn %A Fred S. Roberts %T Full Color Theorems for L(2,1)-Colorings %D March 16, 2000 %Z Thu, 15 Jun 2000 15:00:00 GMT %I DIMACS %R 2000-08 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-08.ps.gz %X The span $\la (G)$ of a graph $G$ is the smallest $k$ for which $G$'s vertices can be $L(2,1)$-colored, i.e., colored with integers in $\{0,1, \ldots, k \}$ so that adjacent vertices' colors differ by at least two, and colors of vertices at distance two differ. $G$ is full-colorable if some such coloring uses all colors in $\{0,1, \ldots, \la (G) \}$ and no others. We prove that all trees except stars are full-colorable. The connected graph $G$ with the smallest number of vertices exceeding $\la (G)$ that is not full-colorable is $C_6$. We describe an array of other connected graphs that are not full-colorable and go into detail on full-colorability of graphs of maximum degree four or less. %A Suh-Ryung Kim %A Fred S. Roberts %T Competition Graphs of Semiorders and the Conditions $C(p)$ and $C^*(p)$ %D March 16, 2000 %Z Wed, 19 Apr 2000 16:00:00 GMT %I DIMACS %R 2000-09 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-09.ps.gz %X Given a digraph $D$, its competition graph has the same vertex set and an edge between two vertices $x$ and $y$ if there is a vertex $u$ so that $(x,u)$ and $(y,u)$ are arcs of $D$. Motivated by a problem of communications, we study the competition graphs of the special digraphs known as semiorders. This leads us to define a conditions on digraphs called $C(p)$ and $C^*(p)$ and to study the graphs arising as competition graphs of acyclic digraphs satisfying conditions $C(p)$ or $C^*(p)$. %A Endre Boros %A Takashi Horiyama %A Toshihide Ibaraki %A Kazuhisa Makino %A Mutsunori Yagiura %T Finding Small Sets of Essential Attributes in Binary Data %D March 17, 2000 %Z Wed, 19 Apr 2000 16:00:00 GMT %I DIMACS %R 2000-10 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-10.ps.gz %X We consider the problem of finding support sets (i.e., sets of essential attributes) in a given data set, which consists of n-dimensional binary vectors of positive examples and negative examples. A set of attributes is a support set if positive examples and negative examples can be separated by using only the attributes in the set. Finding small support sets is an important topic in such fields as knowledge discovery, data mining, learning theory and logical analysis of data. Based on several measures of separation, we discuss why finding small support sets is important, and how to find such sets, together with results of some computational experiment. Theoretical analysis of the approximation ratios of the proposed algorithms is also provided. %A Vince Grolmusz %T A Note on Set Systems with no Union of Cardinality 0 Modulo m %D March 27, 2000 %Z Wed, 19 Apr 2000 16:00:00 GMT %I DIMACS %R 2000-11 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-11.ps.gz %X

Alon, Kleitman, Lipton, Meshulam, Rabin and Spencer (Graphs. Combin. 7 (1991), no. 2, 97-99) proved, that for any hypergraph ${\cal F}=\{F_1,F_2,\ldots, F_{d(q-1)+1}\}$, where $q$ is a prime-power, and $d$ denotes the maximal degree of the hypergraph, there exists an ${\cal F}_0\subset {\cal F}$, such that $|\bigcup_{F\in{\cal F}_0}F|\equiv 0\pmod{q}$. We give a direct, alternative proof for this theorem, and we also give an explicit construction of a hypergraph of degree $d$ and size $\Omega(d^2)$ which does not contain a non-empty sub-hypergraph with a union of size 0 modulo 6.

%A Jie Wu %A Li Sheng %T An Efficient Sorting Algorithm for a Sequence of Kings in a Tournament %D April 4, 2000 %Z Wed, 19 Apr 2000 16:00:00 GMT %I DIMACS %R 2000-12 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-12.ps.gz %X A king $u$ in a tournament is a player who beats ($\rightarrow$) any other player $v$ {\em directly or indirectly}. That is, either $u \rightarrow v$ or there exists a third player $w$ such that $u \rightarrow w$ and $w \rightarrow v$. A sorting sequence of kings in a tournament of $n$ players is a sequence of players, $S=(u_1$, $u_2$, ..., $u_n)$, such that $u_i \rightarrow u_{i+1}$ and $u_i$ in a king in the sub-tournament $T_{u_i}$ induced by $u_i, u_{i+1}, ..., u_n$ for $i=1, 2,..., n-1$. The existence of a sorting sequence of kings in any tournament is shown \cite{LouW00} where a sorting algorithm with a complexity of $\Theta(n^{3})$ is given. In this paper, we present a constructive proof for the existence of a sorting sequence of kings of a tournament and propose an efficient algorithm with a complexity of $\Theta(n^2)$. %A Yuri Levin %A Adi Ben-Israel %T Directional Newton Methods in n Variables %D May 2, 2000 %Z Tue, 2 May 2000 17:00:00 GMT %I DIMACS %R 2000-13 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-13.ps.gz %X

Directional Newton methods for functions $f$ of $n$ variables are shown to converge, under typical assumptions, to a solution of $f(\mathbf{x})=0$. The rate of convergence is quadratic, for near-gradient directions, and directions along components of the gradient of $f$ with maximal modulus. These methods are applied to solving systems of equations without inversion of the Jacobian matrix.

Key words and phrases. Newton Method, Single equations, Systems of equations

Mathematics Subject Classification. Primary 65H05, 65H10; Secondary 49M15

%A Gabriela Alexe %A Sorin Alexe %A Stephan Foldes %A Peter L. Hammer %A Bruno Simeone %T Consensus Algorithms for the Generation of all Maximal Bicliques %D May 22, 2000 %Z Wed, 24 May 2000 15:00:00 GMT %I DIMACS %R 2000-14 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-14.ps.gz %X We describe a consensus-type algorithm for determining all the maximal complete bipartite (not necessarily induced) subgraphs of a graph. We show that by imposing a particular order in which the consensus type operations should be executed, this algorithm becomes totally polynomial. By imposing a further restriction on the way the algorithm has to be executed, we derive an improved variant of it, the complexity of which is bounded by a polynomial that is cubic in the input size, and only linear in the output size, and show its high efficiency on numerous computational experiments on randomly generated graphs with up to 1000 vertices and 6000 edges. %A Yuval Shavitt %A Xiaodong Sun %A Avishai Wool %A Bulent Yener %T Computing the Unmeasured: An Algebraic Approach to Internet Mapping %D May 23, 2000 %Z Wed, 24 May 2000 15:00:00 GMT %I DIMACS %R 2000-15 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-15.ps.gz %X

Distance estimation is important to many Internet applications, most notably for a WWW client that needs to select a server among several potential candidates. Current approaches to distance (i.e., time delay) estimation in the Internet are based on placing Tracer stations in key locations and conducting measurements between them. The Tracers construct an approximated map of the Internet after processing the information obtained from these measurements.

This work presents a novel algorithm, based on Algebraic tools, that computes additional distances, which are not explicitly measured. As such, the algorithm extracts more information from the same amount of measurement data.

Our algorithm has several practical impacts. First, it can reduce the number of Tracers and measurements without sacrificing information. Second, our algorithm is able to compute distance estimates between locations where Tracers cannot be placed. This is especially important when unidirectional measurements are conducted, since such measurements require specialized equipment which cannot be placed everywhere.

To evaluate the algorithm's performance, we tested it both on randomly generated topologies and on real Internet measurements. Our results show that the algorithm computes up to 50-200% additional distances beyond the basic Tracer-to-Tracer measurements.

%A F. Comets %A G. Giacomin %A J.L. Lebowitz %T The Sherrington--Kirkpatrick model with short range ferromagnetic interactions %D June 2, 2000 %Z Thu, 15 Jun 2000 15:00:00 GMT %I DIMACS %R 2000-16 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-16.ps.gz %X

We study a model of Ising spins with short range ferromagnetic and long range SK interactions. We generalize the results obtained for the standard SK model, computing in particular the high temperature pressure.

RÉSUMÉ. Nous étudions un modéle de spins binaires qui est soumis á la fois á des interactions de type Ising et de type Sherrington-Kirkpatrick. Nous généralisons des résultats obtenus dans le cas du modéle SK seul, en calculant en particulier la pression á haute température.

%A Endre Boros %A Vladimir Gurvich %A Leonid Khachiyan %A Kazuhisa Makino %T Generating Weighted Transversals of a Hypergraph %D June 21, 2000 %Z Mon, 26 Jun 2000 15:00:00 GMT %I DIMACS %R 2000-17 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-17.ps.gz %X

We consider a generalization of the notion of transversal to a finite hypergraph, so called {\em weighted transversals}. Given a non-negative weight vector assigned to each hyperedge of the input hypergraph, we define a weighted transversal as a minimal vertex set which intersects a collection of hypereredges of sufficiently large total weight. We show that the hypergraph of all weighted transversals is dual-bounded, i.e, the size of its dual hypergraph is polynomial in the number of weighted transversals and the size of the input hypergraph. Our bounds are based on new inequalities of extremal set theory and threshold Boolean logic, which may be of independent interest. For instance, we show that for any threshold frequency, the number of maximal frequent sets of columns in a binary matrix is bounded by the number of minimal infrequent sets of columns in the same matrix multiplied by the number of its rows. We also prove that the problem of generating all weighted transversals for a given hypergraph is polynomial-time reducible to the generation of all ordinary transversals for another hypergraph, i.e., to the well-known hypergraph dualization problem. As a corollary, we obtain an incremental quasi-polynomial-time algorithm for generating all weighted transversals for a given hypergraph. This result includes as special cases the generation of all the minimal Boolean solutions to a given system of non-negative linear inequalities and the generation of all minimal infrequent sets of columns for a given binary matrix.

%A Shigang Chen %A Yuval Shavitt %T A Scalable Distributed QoS Multicast Routing Protocol %D July 26, 2000 %Z Thu, 3 Aug 2000 15:00:00 GMT %I DIMACS %R 2000-18 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-18.ps.gz %X

Many Internet multicast applications such as teleconferencing and remote diagnosis have Quality-of-Service (QoS) requirements. Such requirements can be additive (end-to-end delay), multiplicative (loss rate) or with a bottleneck nature (bandwidth). For these applications, QoS multicast routing protocols are important in enabling new receivers to join a multicast group. However, current routing protocols are either too restrictive in their search for a feasible path between a new receiver and the multicast tree, or burden the network with excessive overhead.

In this paper we propose S-QMRP, a new Stateless Qos Multicast Routing Protocol that supports all three QoS requirement types. S-QMRP is scalable because it has very small communication overhead and requires no state outside the multicast tree; yet, it retains a high success probability. S-QMRP achieves the favorable tradeoff between routing performance and overhead by carefully selecting the network sub-graph in which it conducts the search for a path that can support the QoS requirement, and by auto-tuning the selection according to the current network conditions. S-QMRP does not require any global network state to be maintained and can operate on top of any unicast routing protocol. Our extensive simulation shows that S-QMRP performs better than the previously suggested protocols.

%A A. Barg %A D. Nogin %T Bounds for Packings of Spheres in the Grassmann Manifolds %D July 27, 2000 %Z Sat, 5 Aug 2000 13:00:00 GMT %I DIMACS %R 2000-19 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-19.ps.gz %X

We derive the Varshamov--Gilbert and Hamming bounds for packings of spheres (codes) in the Grassmann manifolds over $\mathbb R$ and $\mathbb C$. The distance between two $k$-planes is defined as $\rho(p,q)=(\sin^2\theta_1+\dots+\sin^2\theta_k)^{1/2}$, where $\theta_i, 1\le i\le k$, are the principal angles between $p$ and $q$.

%A A. Barg %A G. Cohen %A S. Encheva %A G. Kabatiansky %A G. Zemor %T A Hypergraph Approach to the Identifying Parent Property: the Case of Multiple Parents %D July 27, 2000 %Z Fri, 11 Aug 2000 15:00:00 GMT %I DIMACS %R 2000-20 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-20.ps.gz %X

Let $C$ be a code of length $n$ over an alphabet of $q$ letters. A codeword $y$ is called a descendant of a set of $t$ codewords $ x^1,\dots,x^t$ if $y_i\in\{x^1_i,\dots,x^t_i\}$ for all $i=1,\dots,n.$ A code is said to have the identifiable parent property if for any $n$-word that is a descendant of at most $t$ parents it is possible to identify at least one of them. We prove that for any $t\le q-1$ there exist sequences of such codes with asymptotically nonvanishing rate.

%A E. Boros %A K. Elbassioni %A V. Gurvich %A L. Khachiyan %T An Incremental RNC Algorithm for Generating All Maximal Independent Sets in Hypergraphs of Bounded Dimension %D August 3, 2000 %Z Sat, 5 Aug 2000 13:00:00 GMT %I DIMACS %R 2000-21 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-21.ps.gz %X

We show that for hypergraphs of bounded edge size, the problem of extending a given list of maximal independent sets is NC-reducible to the computation of an arbitrary maximal independent set for an induced sub- hypergraph. The latter problem is known to be in RNC. In particular, our reduction yields an incremental RNC dualization algorithm for hypergraphs of bounded edge size, a problem previously known to be solvable in polynomial incremental time. We also give a similar parallel algorithm for the dualization problem on the product of arbitrary lattices which have a bounded number of immediate predecessors for each element.

%A Alexander Kelmans %A Dhruv Mubayi %A Benny Sudakov %T Asymptotically Optimal Tree--Pacings in Regular Graphs %D August 8, 2000 %Z Tue, 8 Aug 2000 22:00:00 GMT %I DIMACS %R 2000-22 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-22.ps.gz %X

Let $T$ be a tree with $t$ vertices. Clearly, an $n$ vertex graph contains at most $n/t$ vertex disjoint trees isomorphic to $T$. In this paper we show that for every $\ep>0$, there exists a $D(\ep,t)>0$ such that, if $d>D(\ep,t)$ and $G$ is a simple $d$-regular graph on $n$ vertices, then $G$ contains at least $(1-\ep)n/t$ vertex disjoint trees isomorphic to $T$.

Keywords: graph, hypergraphs, packing, trees, matchings

%A Alexander Kelmans %A Dhruv Mubayi %T How Many Disjoint 2--edge Paths Must a Cubic Graph Have? %D August 10, 2000 %Z Fri, 11 Aug 2000 15:00:00 GMT %I DIMACS %R 2000-23 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-23.ps.gz %X

In this paper we show that every simple cubic graph on $n$ vertices has a list of at least n/4 disjoint 2-edge paths and that this bound is sharp. Our proof provides a polynomial time algorithm for finding such a list in a simple cubic graph.

Keywords: packing, 2--edge path, cubic graph, polynomial time algorithm.

%A Boris Galitsky %T Question-Answering System for Teaching Autistic Children to Reason about Mental States %D August 27, 2000 %Z Sun, 3 Sep 2000 18:00:00 GMT %I DIMACS %R 2000-24 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-24.ps.gz %X

We build the natural language question-answering system to teach autistic patients reasoning about mental states. In accordance to our model of autism disorder, some reasoning patterns concerning perception of the concepts of knowing, believing and intention are corrupted. Based on this model, we have suggested the autism diagnosis and reasoning rehabilitation strategy, where the professional psychologists explained the autistic children the set of multi-agent scenarios. Experiments showed that acquiring of mental concepts based on our formalism helps autistic children not only to improve judgment interacting with other people, but also to stimulate the emotional development.

Further evaluation of the model and rehabilitation technology is conducted with automatic training toolkit, implemented on the Internet. Asking questions about mental states of heroes of the scene or textual scenarios assists the revealing and training of the corrupted autistic reasoning. Natural language technology of semantic headers is applied, where the textual answer (explanation) is assigned with a mental formula, which is matched against the representation of an input question or command.

%A A.A. Sapozhenko %T On the Number of Independent Sets in Bipartite Graphs with %D August 27, 2000 %Z Mon, 28 Aug 2000 18:00:00 GMT %I DIMACS %R 2000-25 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-25.ps.gz %X

The asymptotics of the independent set number is found for bipartite graphs which minimum degree is equal in order to the number of vertices.

%A Piotr Berman %A Bhaskar DasGupta %A S. Muthukrishnan %T On the Exact Size of the Binary Space Partitioning of Sets of Isothetic Rectangles with Applications %D September 12, 2000 %Z Fri, 29 Sep 2000 02:00:00 GMT %I DIMACS %R 2000-26 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-26.ps.gz %X

We show an upper bound of 3n on size of the Binary Space Partitioning (BSP) tree for a set of n isothetic rectangles, and an upper bound of 2n if the rectangles tile the underlying space. This improves the previous bounds of 4n. The BSP tree is one of the most popular data structures and even ``small'' factor improvements of 4/3 or 2 we show improves the performance of applications relying on the BSP tree. Furthermore, our upper bounds yield improved approximation algorithms for several rectangular tiling problems in the literature. We also a show a lower bound of 2n in the worst case for a BSP for n isothetic rectangles, and a lower bound of 1.5n if they must form a tiling of the space.

%A Karhan Akcoglu %A James Aspnes %A Bhaskar DasGupta %A Ming-Yang %T Opportunity Cost Algorithms for Combinatorial Auctions %D September 19, 2000 %Z Fri, 29 Sep 2000 02:00:00 GMT %I DIMACS %R 2000-27 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-27.ps.gz %X

Two general algorithms based on opportunity costs are given for approximating a revenue-maximizing set of bids an auctioneer should accept, in a combinatorial auction in which each bidder offers a price for some subset of the available goods and the auctioneer can only accept non-intersecting bids. Since this problem is difficult even to approximate in general, the algorithms are most useful when the bids are restricted to be connected node subsets of an underlying object graph that represents which objects are relevant to each other. The approximation ratios of the algorithms depend on structural properties of this graph and are small constants for many interesting families of object graphs. The running times of the algorithms are linear in the size of the bid graph, which describes the conflicts between bids. Extensions of the algorithms allow for efficient processing of additional constraints, such as budget constraints that associate bids with particular bidders and limit how many bids from a particular bidder can be accepted.

%A Xiaodong Sun %T Explicit Interpolation Sets Using Perfect Hash Families %D October 9, 2000 %Z Mon, 30 Oct 2000 22:00:00 GMT %I DIMACS %R 2000-28 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-28.ps.gz %X Let $S$ be a set of functions with common domain $D$. We say $X$, a subset of $D$, an interpolation set for $S$ if the values on $X$ uniquely determine a function $f$ in $S$. Recently, Piotr Indyk gave an explicit construction of interpolation sets of size $O(k^4 \log ^4 n)$ for the family of boolean functions on $n$ variables which depend symmetrically on at most $k$ variables. Using perfect hash families, we have a variant of Indyk's method to get an explicit construction of interpolation sets of size $O(k^{10}\log n\log\log n/\log\log\log n)$ for this family of functions. %A Boris Galitsky %T Technique of semantic headers: a manual for knowledge engineers %D November 20, 2000 %Z Tue, 21 Nov 2000 02:00:00 GMT %I DIMACS %R 2000-29 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-29.ps.gz XX This manual addresses the issues of knowledge representation in the form of semantic headers (SH) for conversion of a textual document into a form, appropriate for question answering. A set of semantic headers is intended to formally represent the essential idea of a document with respect to possible questions, such that this document would serve as an answer. The knowledge base then includes the textual answers, structured by means of assigned semantic headers. The formal representation of the natural language (NL) query is then matched against the knowledge base in the form of a set of these headers. The logical mechanisms of matching query translations against semantic headers and derivation of semantic headers themselves is presented, as well as applications of meta-reasoning, default reasoning, reasoning about action and time, and graph representation of answer classification.

This technique shows superior performance over the knowledge systems based on syntactic matching of NL queries with the prior prepared NL representation of canonical queries, and the knowledge systems based on the fully formalized knowledge. Our approach gives the higher precision of answers than the former one because it involves the semantic information in higher degree. At the same time, in the logically complex and poorly structured domains SH technique gives more complete answers, possesses higher consistency to context deviation and is more efficient than the latter approach because the full knowledge formalization is not required.

The manual of semantic header technique is intended to assist the linguists and knowledge engineers in the creation of question answering systems for the sophisticated vertical domains. The manifold of coding samples and extended discussions help to deeper understand the peculiarities of using logic programming in the knowledge representation. The tutorial part is followed by the qualification test using the multiple-choice questions. %A Larry Shepp %T A Model for Stock Price Fluctuations Based on Information %D October 19, 2000 %Z Mon, 30 Oct 2000 22:00:00 GMT %I DIMACS %R 2000-30 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-30.ps.gz %X This paper is dedicated to the memory of Aaron Wyner, the well known information theorist. It gives a new model for stock price fluctuations based on a concept of ``information''. In contrast, the usual Black-Scholes-Merton-Samuelson model is based on the {\em explicit} assumption that information plays {\em no} role in stock prices. The new model is based on the non-uniformity of information in the market and the time delay until new information becomes generally known.

The new model is expected to give more accurate predictions of future prices and more accurate formulas for hedge option valuations. The new valuations have been calculated for the various standard options inside the new model in a recent PhD thesis by Xin Guo. Because the concept of information is the driving one in the new model it seemed appropriate to discuss this in the present volume even though ``information'' is used in a somewhat different sense here than in communication theory.

In communication theory, information is {\em intended} to be communicated. One is concerned with designing a means for the successful transfer of messages from a source to the receiver and the value of the information is in its successful transmission. In the stock market, the reverse is usually true; information is hoarded and is of value to the owner {\em only} until it becomes known to others. Some messages are avidly communicated in the market but are really meant to {\em disinform} the receivers. This may of course also be true occasionally in communication theory which usually avoids concerning itself with the {\em meaning} of the message to be transmitted. Despite these differences in the role of information in the two situations, there are similarities in the mathematics used to study them. Certainly probabilistical models play a prominent role in both theories.

In Shannon's communication theory quantitative value is assigned to a channel (its rate or its capacity). Is there anything similar in the market? We are able to assign a quantitative value to knowing an item of information {\it which is unknown to others} say that a company is in a strong (or weak) position at a given point in time, via pricing of options on the company's stock. This paper is intended as a first step towards the goal of making the use of information into a quantitative tool.

Problems with explicit solutions are of value in obtaining insights. At the end of the paper we compare several problems of mathematical interest in order to better understand which optimal stopping problems have explicit solutions. %A S. Bastea %A R. Esposito %A J. L. Lebowitz %A R. Marra %T Binary Fluids with Long Range Segregating Interaction I: Derivation of Kinetic and Hydrodynamic Equations %D October 24, 2000 %Z Tue, 21 Nov 2000 02:00:00 GMT %I DIMACS %R 2000-31 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-31.ps.gz %X We study the evolution of a two component fluid consisting of ``blue'' and ``red'' particles which interact via strong short range (hard core) and weak long range pair potentials. At low temperatures the equilibrium state of the system is one in which there are two coexisting phases. Under suitable choices of space-time scalings and system parameters we first obtain (formally) a mesoscopic kinetic Vlasov-Boltzmann equation for the one particle position and velocity distribution functions, appropriate for a description of the phase segregation kinetics in this system. Further scalings then yield Vlasov-Euler and incompressible Vlasov-Navier-Stokes equations. We also obtain, via the usual truncation of the Chapman-Enskog expansion, compressible Vlasov-Navier-Stokes equations. %A Peter C. Fishburn %A Fred S. Roberts %T Minimal Forbidden Graphs for L(2,1)-Colorings %D October 30, 2000 %Z Mon, 30 Oct 2000 22:00:00 GMT %I DIMACS %R 2000-32 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-32.ps.gz %X The span $\lambda(G)$ of a graph G is the smallest k for which G's vertices can be L(2,1)-colored, i.e., colored with integers in {0,1,...,k} so that adjacent vertices' colors differ by as least two, and colors of vertices at distance two differ. We study minimal forbidden graphs, graphs with the property that every proper subgraph has smaller span. Fixing the maximum degree, we observe that the first nontrivial case involves minimal forbidden graphs of maximum degree 3 and span 5. We present examples to illustrate the variety of graphs with this property and in particular provide several infinite families of such graphs. %A E. Boros %A V. Gurvich %A R. Meshulam %T Difference Graphs %D November 1, 2000 %Z Tue, 21 Nov 2000 02:00:00 GMT %I DIMACS %R 2000-33 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-33.ps.gz %X Intersection and measured intersection graphs are quite common in the literature. In this paper we introduce the analogous concept of measured difference graphs: Given an arbitrary hypergraph $\cH = \{H_1,...,H_n\}$, let us associate to it a graph on vertex set $[n]=\{1,2,...,n\}$ in which $(i,j)$ is an edge iff the corresponding sets $H_i$ and $H_j$ are ``sufficiently different''. More precisely, given an integer threshold $k$, we consider three definitions, according to which $(i,j)$ is an edge iff (1) $|H_i \setminus H_j| + |H_j \setminus H_i| \geq 2k$, (2) $max\{|H_i \setminus H_j|,|H_j \setminus H_i|\} \geq k$, and (3) $min\{|H_i \setminus H_j|,|H_j \setminus H_i|\} \geq k$. It is not difficult to see that each of the above define hereditary graph classes, which are monotone with respect to $k$. We show that for every graph $G$ there exists a large enough $k$ such that $G$ arises with any of the definitions above. We prove that with the first two definitions one may need $k=\Omega(\log n)$ in any such realizations of certain graphs on $n$ vertices. However, we do not know a graph $G$ which could not be realized by the last definition with $k=2$. %A Srikrishna Divakaran %A Michael Saks %T An Online Scheduling Problem with Job Set-ups %D November 13, 2000 %Z Tue, 21 Nov 2000 02:00:00 GMT %I DIMACS %R 2000-34 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-34.ps.gz %X Machine scheduling and paging are two fundamental problems that have been studied extensively from the view of online algorithms. In both problems, one processes a sequence $J_1,\ldots,J_n$ of {\em jobs} (or {\em page requests}) that arrive over time. In the paging problem, requests must be answered in the order of arrival because the requests arise in the context of the execution of a sequential program. The need for decision making comes from the presence of a cache which can store a limited number of pages, where serving a cached page is considerably cheaper than an uncached one. Thus algorithms for paging are focused around the choice of caching policy. In scheduling, there is no cache, but the scheduler has (at least limited) freedom to reorder the jobs, and choosing the order is the major issue in the design of online scheduling algorithms. In computer systems, however, there are important situations where both caching and job reordering are available. One very natural setting where this happens is handling web page requests at a high volume web site. As in the usual paging problem, the server must manage a cache. But here the requests are (essentially) independent, so the server is free to reorder them.

In this paper, we begin the study of online algorithms for scheduling systems where both caching and reordering are available. We consider a simple, but already interesting and nontrivial, case: that of a single machine with a cache of unit size, and uniform page size. This particular special case is also natural in the usual machine scheduling context where jobs are classified into one of $\{1,2,...,F\}$ job types, and before processing a job, the machine must be configured (or set-up) according to the type of the job. This configuring (or set-up) is required unless the previously served job is of the same type as the current one. The current configuration of the machine in this scheduling problem, corresponds exactly to the contents of the unit cache in the page server problem.

In this context, we consider the online problem of scheduling a sequence $J=(J_{1},J_{2},...,J_{N})$ of jobs with release times, processing times and sequence independent set-up times, on a single machine, to minimize the maximum flow time. A partitioning of the jobs into $F$ job types is given. A set-up is required at the start of each batch, where a batch is the largest set of contiguously scheduled jobs of the same job type. This problem is a special case of the maximum lateness problem, a problem known to be $NP$-hard even for very restrictive special cases and for which there are no known polynomial time $O(1)$ approximation algorithms. In this paper, we present a polynomial time $O(1)$-competitive online algorithm for the maximum flow time problem and also prove the $NP$-Hardness of the offline version of this problem. %A Oliver Penrose %A George Stell %T Close to close packing %D November 13, 2000 %Z Tue, 21 Nov 2000 02:00:00 GMT %I DIMACS %R 2000-35 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-35.ps.gz %X For various lattice gas models with nearest neighbour exclusion (and, in one case, second-nearest neighbour exclusion as well), we obtain lower bounds on $m$, the average number of particles on the non-excluded lattice sites closest to a given particle. They are all of the form $$ m/m_{cp} \ge 1 - \hbox{~const.}(N_{cp}/N - 1) $$ where $N$ is the number of occupied sites, $m_{cp}$ is the coordination number, snd $N_{cp}$ is the value of $N$ at close packing. An analogous result exists for hard disks in the plane. %A E. Boros ,V. Gurvich %A L. Khachiyan %A K. Makino %T An inequality limiting the number of maximal frequent sets %D November 13, 2000 %Z Tue, 21 Nov 2000 02:00:00 GMT %I DIMACS %R 2000-37 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-37.ps.gz %X Given an arbitrary $m\times n$ binary matrix $A$ and a threshold $t \in \{1, \ldots, m\}$, a subset $C$ of the columns is called $t$-{\em frequent} if there are at least $t$ rows having a $1$ in each of these columns, and otherwise $C$ is called $t$-{\em infrequent}. Denoting by $\alpha$ the number of maximal $t$-frequent, and by $\beta$ the number of minimal $t$-infrequent column sets in the given matrix $A$, we prove that the inequality $\alpha \leq (m-t+1)\beta$ holds. This inequality is sharp, and allows for an incremental quasi-polynomial algorithm for generating all minimal $t$-infrequent sets, while the analogous problem for maximal $t$-frequent sets is NP-hard. Our proof is based on an inequality from extremal set theory, which may be of independent interest. %A Ayman Khalfalah %A Sachin Lodha %A Endre Szemeredi %T Tight Bound for the Density of Sequences of Integers the Sum of No Two of which is a Perfect Square %D November 16, 2000 %Z Tue, 21 Nov 2000 02:00:00 GMT %I DIMACS %R 2000-39 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-39.ps.gz %X P. Erd\H{o}s and D. Silverman~\cite{eg-80} proposed the problem of determining the maximal density attainable by a set $S$ of positive integers having the property that no two distinct elements of $S$ sum up to a perfect square. J. P. Massias exhibited such a set consisting of all $x \equiv 1$ (mod $4$) with $x \equiv 14, 26, 30$ (mod $32$) in~\cite{m}. In~\cite{los-82}, J. C. Lagarias, A. M. Odylzko and J. B. Shearer showed that for any positive integer $n$, one cannot find more than $\frac{11}{32} n$ residue classes (mod $n$) such that the sum of any two is never congruent to a square (mod $n$), thus essentially proving that the Massias' set has the best possible density. They~\cite{los-83} also proved that the density of such a set $S$ is never more than $0.475$ when we allow general sequences.

We improve on the lower bound for general sequences, essentially proving that it is not $0.475$, but arbitrarily close to $\frac{11}{32}$, the same as that for sequences made up of only arithmetic progressions. %A Tiina Heikkinen %T Resource Allocation in a Distributed Network %D November 17, 2000 %Z Tue, 21 Nov 2000 02:00:00 GMT %I DIMACS %R 2000-40 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-40.ps.gz %X

This paper discusses distributed resource allocation in a communication system. Some recent approaches to decentralized resource allocation in a communication system are summarized. A characterization for resource control and pricing in a distributed wireless network with transmit power control is presented.

Power control is modelled as a noncooperative externality game between the users. In the absence of a price each user has the incentive to increase the transmit power to increase the quality-of service as measured by the signal-to-noise ratio. However, the increase in transmission energy of a representative user by definition deteriorates the signal-to-noise ratio for all other users, thus imposing an externality cost. The Nash equilibrium in an uncontrolled distributed network is one where the system fails due to excessive congestion. However, by introducing a simple linear pricing penalty, the distributed system can be made to achieve the Pareto-optimal quality of service.

Convergence to an efficient Nash equilibrium under pricing is observed in a numerical example assuming that the users apply a standard learning automaton.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-40.ps.gz %A F. R. McMorris %A Fred S. Roberts %A Chi Wang %T The Center Function on Trees %D December 7, 2000 %Z Fri, 15 Dec 2000 22:00:00 GMT %I DIMACS %R 2000-41 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-41.ps.gz %X When $(X, d)$ is a finite metric space and $\pi = (x_1 , \ldots, x_k ) \in X^k$, a central element for $\pi$ is an element $x$ of $X$ for which max$\{ d(x, x_i ): i = 1 ,\ldots ,k\}$ is minimum. The function that returns the set of all central elements for any tuple $\pi$ is called the center function on $X$. In this note, the center function on finite trees is characterized. %A Italo J. Dejter %T Perfect Dominating Sets of Grids %D December 13, 2000 %Z Fri, 15 Dec 2000 22:00:00 GMT %I DIMACS %R 2000-42 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-42.ps.gz %X Let m and n be positive integers. The algorithmic search for perfect dominating sets of the rectangular grid G(m,n) with an initial condition S' defined as an admissible subset of a side G(m,1) of G(m,n) is considered. A binary decision algorithm that generates all perfect dominating sets of G(m,n) satisfying (or containing) such S' is presented, and some related questions and conjectures are posed, leading to consideration of their periodic extendibility to the plane lattice as well as to extremal properties of the grid depth n for a fixed grid width m under the presence of such dominating sets. %A Ashwin Nayak %A Ashvin Vishwanath %T Quantum Walk on the Line %D December 13, 2000 %Z Fri, 15 Dec 2000 22:00:00 GMT %I DIMACS %R 2000-43 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-43.ps.gz %X Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider {\em quantum\/} walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example of a typical walk, the ``Hadamard walk''. In particular, we show that after~$t$ time steps, the probability distribution on the line induced by the Hadamard walk is almost uniformly distributed over the interval~$[-t/\sqrt{2},\;t/\sqrt{2}]$. This implies that the same walk defined on the circle mixes in {\em linear\/} time. This is in direct contrast with the quadratic mixing time for the corresponding classical walk. We conclude by indicating how our techniques may be applied to more general graphs. %A Ashwin Nayak %A Ashvin Vishwanath %T Quantum Walk on the Line %D December 13, 2000 %Z Fri, 15 Dec 2000 22:00:00 GMT %I DIMACS %R 2000-43 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-43.ps.gz %X Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider {\em quantum\/} walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example of a typical walk, the ``Hadamard walk''. In particular, we show that after~$t$ time steps, the probability distribution on the line induced by the Hadamard walk is almost uniformly distributed over the interval~$[-t/\sqrt{2},\;t/\sqrt{2}]$. This implies that the same walk defined on the circle mixes in {\em linear\/} time. This is in direct contrast with the quadratic mixing time for the corresponding classical walk. We conclude by indicating how our techniques may be applied to more general graphs. %A Alexander Kelmans %T Packing Trees in Graphes %D December 15, 2000 %Z Fri, 15 Dec 2000 22:00:00 GMT %I DIMACS %R 2000-44 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-44.ps.gz %X Let ${\cal G}^s_r $ denote the set of graphs with each vertex of degree at least $r$ and at most $s$, $v(G)$ the number of vertices, and $\tau _k (G)$ the maximum number of disjoint $k$--edge trees in $G$. In this paper we show that \\[0.5ex] $(a1)$ if $G \in {\cal G}^s_2 $ and $s \ge 4$ then $\tau _2 (G) \ge v(G)/(s+1)$, \\[0.5ex] $(a2)$ if $G \in {\cal G}^3_2 $ and $G$ has no 5--vertex components then $\tau _2 (G) \ge v(G)/4$, \\[0.5ex] $(a3)$ if $G \in {\cal G}^s_1 $ and $G$ has no $k$--vertex component where $k \ge 2$ and $s \ge 3$ then $\tau _k(G) \ge (v(G) - k)/(sk - k +1)$, and \\[0.5ex] $(a3)$ the above bounds are attained for infinitely many connected graphs. \\[0.5ex] \indent Our proofs provide polynomial time algorithms for finding the corresponding packings in a graph. %A I. E. Zverovich %A I. I. Zverovich %T On the ratio of the stability number and the domination number %D January 5, 2000 %Z Fri, 2 Feb 2001 01:00:00 GMT %I DIMACS %R 2000-45 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-45.ps.gz %X Let $\alpha(G)$ and $\gamma(G)$ be the stability number and domination number of a graph $G$, respectively. Since $\alpha(G) \ge \gamma(G)$, $\alpha(G)/\gamma(G) \ge 1$. For each $r \ge 1$, we define a graph $G$ to be an {\em $\alpha/\gamma \le r$-perfect graph} if $\alpha(H)/\gamma(H) \le r$ for each induced subgraph $H$ of $G$.

We show that the class of all $\alpha/\gamma \le r$-perfect graphs is determined by a unique forbidden induced subgraph.

It gives the possibility to approximate $\alpha(G)$ and $\gamma(G)$ in the corresponding classes. %A I. E. Zverovich %T Graph Bipartition with Hereditary Properties %D January 5, 2000 %Z Fri, 2 Feb 2001 01:00:00 GMT %I DIMACS %R 2000-46 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-46.ps.gz %X

A hereditary class $P$ is called {\it finitely generated} if the set of all minimal forbidden induced subgraphs for $P$ is finite. For a pair of hereditary classes $P$ and $Q$, we define a hereditary class $P * Q$ of all graphs $G$ which have a partition $A \cup B = V(G)$ such that $G(A) \in P$ and $G(B) \in Q$ ($G(X)$ is the subgraph of $G$ induced by $X \subseteq V(G)$). We investigate the problem of recognizing finitely generated classes of the form $P * Q$.

We use the following model. Let $H^0$ and $H^1$ be hypergraphs with the same vertex set $V$. The ordered pair $H = (H^0, H^1)$ is called a {\em bihypergraph}. A bihypergraph $H = (H^0, H^1)$ is called {\em bipartite} if there is an ordered partition $V^0 \cup V^1 = V(H)$ such that $V^i$ is stable in $H^i$, $i = 0, 1$. If the maximum cardinality of hyperedges in $H$ is at most $r$ and every $k$-subset of $V(H)$ contains at least one hyperedge then $H \in C(k, r)$.

We prove that there exists a finite number of minimal non-bipartite bihypergraphs in $C(k, r)$ (when $k$ and $r$ are fixed).

Let $P$ and $Q$ be hereditary classes of graphs. Suppose that the stability number $\alpha (H)$ is bounded above for all $H \in P$, and the clique number $\omega (H)$ is bounded above for all $H \in Q$. An ordered partition $A \cup B = V(G)$ is called a {\it ramseian $P * Q$-partition} if $G(A) \in P$ and $G(B) \in Q$. Let ${\rm Ramsey}(P * Q)$ be the set of all graphs which have a ramseian $P * Q$-partition.

Generalizing a result of Gy\'arf\'as \cite{Gyarfas98}, we prove that if both $P$ and $Q$ are finitely generated then ${\rm Ramsey}(P * Q)$ is also finitely generated. In particular, every class of $(\alpha, \beta)$-polar graphs (which are generalizations of split graphs) has a finite forbidden induced subgraph characterization. %A Danny Dolev %A Osnat Mokryn %A Yuval Shavitt %A Innocenty Sukhov %T An Integrated Architecture for the Scalable Delivery of %D January 5, 2000 %Z Fri, 2 Feb 2001 01:00:00 GMT %I DIMACS %R 2000-47 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-47.ps.gz %X The competition on clients attention requires sites to update their content frequently. As a result, a large percentage of web pages are semi-dynamic, i.e., change quite often and stay static between changes. The cost of maintaining consistency for such pages discourages caching solutions. We suggest here an integrated architecture for the scalable delivery of frequently changing hot pages. Our scheme enables sites to dynamically select whether to cyclically multicast a hot page or to unicast it, and to switch between multicast and unicast mechanisms in a transparent way. Our scheme defines a new protocol, called HTTPM. In addition, it uses currently deployed protocols, and dynamically directs browsers seeking for a URL to multicast channels, while using existing DNS mechanisms. Thus, we enable sites to deliver content to a growing amount of users at less cost and during denial of service attacks, while reducing load on core links. We report simulation results that demonstrate the advantages of the Integrated architecture, and its significant impact on server and network load, as well as clients delay. %A Vadim Mottl %A Sergey Dvoenko %A Oleg Seredin %A Casimir Kulikowski %A Ilya Muchnik %T Alignment scores in a regularized support vector classification method for fold recognition of remote protein families %D January 5, 2001 %Z Fri, 2 Feb 2001 01:00:00 GMT %I DIMACS %R 2001-01 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-01.ps.gz %X

One of fundamental principles of molecular biology says that the primary structure of a protein, i.e. sequence of amino acid residues forming its polypeptide chain, carries an essential amount of information for unambiguous establishing its spatial structure. Despite the fact that each protein has its own spatial structure, it is typical phenomenon that the fold pattern remains basically the same within large groups of evolutionarily allied proteins, so that the "number" of essentially different spatial structures is much less than that of known proteins. Since spatial structures are classified in that or other manner, the estimation of the spatial structure of a given protein reduces to its allocating over a finite set of classes, i.e. the problem falls into the competence area of pattern recognition.

The traditional methodology of pattern recognition presupposes that the object whose class-membership is to be recognized is represented by vector of some numerical features and is considered as a point in the respective linear vector space. However, the actual diversity of amino acid properties that may play an important part in forming the spatial structure of a protein is so immensely rich, that the choice of suitable numerical properties makes a special problem which is the key one here. We consider here an alternative featureless approach to recognition of spatial structure of proteins. It is proposed to judge about the membership of a protein in one of the classes of spatial structures immediately on the basis of measuring the proximity of its amino acid chain to those of some other proteins whose spatial structure is known.

To infer the decision rule of recognition from a training sample of proteins of known structure, we apply the traditional support vector method of machine learning on the basis of treating amino acid chains as elements of a Hilbert space, i.e. linear space with inner product, in what role the pairwise alignment scores are used. The inevitable difficulty of the small size of training samples is overcome by a special regularization technique that makes use of some available a priori information on the sought-for decision rule.

The proposed approach to the problem of fold class recognition illustrated by results of processing a collection of 396 mutually distant protein domains of 51 fold classes chosen from the SCOP database. %A Leonid Shvartser %A Casimir Kulikowski %A Ilya Muchnik %T Multiple sequence alignment using the quasi-concave function optimization based on the DIALIGN combinatorial structures %D January 5, 2001 %Z Fri, 2 Feb 2001 01:00:00 GMT %I DIMACS %R 2001-02 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-02.ps.gz %X Multiple sequence alignment is usually considered as an optimization problem, which has a statistical and a structural component. It is known that in the problem of protein sequence alignment a processed sample is too small and not representative in the statistical sense though this information can be sufficient if an appropriate structural model is used. In order to utilize this information a new structural description of the pairwise alignment results union has been developed. It is shown that if the structure is restored then Multiple Sequence Alignment is achieved. Introduced structure represents the set of local maximums of quasi-concave set function on a lower semi lattice, which in turn is a union of the set-theoretical intervals. This union is a set of the consistent subsets of diagonals, introduced by B. Morgenstern, A. Dress, and T. Werner (1996). Algorithm for local maximums search on proposed structure has been developed. It consists of an alternation of the Forward and Backward passes. The Backward pass in this algorithm is a rigorous while the Forward pass is based on heuristics. Multiple alignment of 5 protein sequences are used as an illustration of the proposed algorithm. %A Vince Grolmusz %T Constructing Set-Systems with Prescribed Intersection Size %D January 11, 2001 %Z Fri, 2 Feb 2001 01:00:00 GMT %I DIMACS %R 2001-03 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-03.ps.gz %X Let $f$ be an $n$ variable polynomial with positive integer coefficients, and let ${\cal H}=\{H_1,H_2,\ldots,H_m\}$ be a set-system on the $n$-element universe. We define set-system $f({\cal H})=\{G_1,G_2,\ldots,G_m\}$, and prove that $f(H_{i1}\cap H_{i2}\cap\ldots\cap H_{ik})=|G_{i1}\cap G_{i2}\cap\ldots\cap G_{ik}|$, for any $1\leq k\leq m$, where $f(H_{i1}\cap H_{i2}\cap\ldots\cap H_{ik})$ denotes the value of $f$ on the characteristic vector of $H_{i1}\cap H_{i2}\cap\ldots\cap H_{ik}$.

The construction of $f({\cal H})$ is a straightforward polynomial--time algorithm from ${\cal H}$ and polynomial $f$. In this paper we use this algorithm for constructing set-systems with prescribed intersection sizes modulo an integer.

As a by-product of our method, some Ray-Chaudhuri--Wilson-like theorems are proved. %A Vince Grolmusz %T Set-Systems with Restricted Multiple Intersections and Explicit Ramsey Hypergraphs %D January 11, 2001 %Z Fri, 2 Feb 2001 01:00:00 GMT %I DIMACS %R 2001-04 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-04.ps.gz %X We give generalizations for the Deza-Frankl-Singhi Theorem in case of multiple intersections. More exactly, we prove, that if ${\cal H}$ is a set-system, which satisfies that for some $k$, that the $k$-wise intersections occupy only $\ell$ residue-classes modulo a $p$ prime, while the sizes of the members of ${\cal H}$ are not in these residue classes, then the size of ${\cal H}$ is at most $$(p-1)(k-1)\sum_{i=1}^{|L|}{n\choose i}$$ This result strengthtens a result of F\"uredi (1983), and gives partial answer to a question of T. S\'os (1976).

As an application, we give explicit constructions for (multi-colored) Ramsey hypergraphs. By our best knowledge, this is the first explicit construction of a Ramsey-hypergraph in the literature. %A Italo J. Dejter %T Distribution of Distances in Star Graphs %D January 22, 2001 %Z Fri, 2 Feb 2001 01:00:00 GMT %I DIMACS %R 2001-05 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-05.ps.gz %X The distribution of distances in the star graph ST_n, where n is an integer >1, is determined from any fixed vertex, in particular to the vertices of each one of the n so-called efficient dominating sets, or 1-perfect codes. %A I. E. Zverovich %T Weighted well-covered graphs and complexity questions %D February 6, 2001 %Z Thu, 5 Apr 2001 05:00:00 GMT %I DIMACS %R 2001-06 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-06.ps.gz %X

A weighted graph G is called well-covered if all its maximal stable sets have the same weight. This common weight is the value of G. Let S be a stable set of G (possibly, $S = \emptyset$). The subgraph $G - N[S]$ is called a co-stable subgraph of G. We denote by Sub(G) the set of all co-stable subgraphs of G (considered up to isomorphism). A class of weighted graphs P is called co-hereditary if it is closed under taking co-stable subgraphs, i.e., $G \in \mathcal{P}$ implies ${\rm CSub}(G) \subseteq \mathcal{P}$.

We note that the class $\mathcal{WW}$ of all weighted well-covered graphs is co-hereditary and characterize $\mathcal{WW}$ in terms of forbidden co-stable subgraphs.

Then we use a reduction from Satisfiability to show that the following decision problems are NP-complete.

Decision Problem 1 (Co-Stable Subgraph).
Instance: A graph $G$ and a set $U \subseteq V(G)$ that induces a subgraph $H$.
Question: Is $H$ a co-stable subgraph of $G$?

Decision Problem 2 (Co-Stable Subgraph $H$).
Instance: A graph $G$.
Question: Is $H$ a co-stable subgraph of $G$?

Let $\Delta(G)$ be the maximum vertex degree of a graph $G$. We show that recognizing weighted well-covered graphs with bounded $\Delta(G)$ can be done in polynomial time. %A I. E. Zverovich %A I. I. Zverovich %T Finding a maximum stable set in pentagraphs %D February 6, 2001 %Z Thu, 5 Apr 2001 05:00:00 GMT %I DIMACS %R 2001-07 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-07.ps.gz %X

Penta is the configuration shown in Figure 1(a), where continuous lines represent edges and dotted lines represent non-edges. The vertex $u$ in Figure 1(a) is called the center of Penta. A graph $G$ is called a pentagraph if every induced subgraph $H$ of $G$ has a vertex $v$ which is not a center of induced Penta in $H$.

The class of pentagraphs is a common generalization of chordal (triangulated) graphs and Mahadev graphs.

We construct a polynomial-time algorithm that either find a maximum stable set of $G$ or concludes that $G$ is not a pentagraph. %A Boris Galitsky %A Sergey Shelepin %T On the inter-residue correlation patterns and their role in classification of protein families %D February 9, 2001 %Z Thu, 5 Apr 2001 05:00:00 GMT %I DIMACS %R 2001-08 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-08.ps.gz %X

We build a novel method to calculate and analyze the correlations in mutational behavior between different positions in a multiple sequence alignment. The inter-dependence between the residues for a protein family is represented as a matrix of correlation values obeying the invariance with respect to specific amino acids, the number of sequences representing a family, the length of sequences, residue variability and the uniformity of data set representation. Common and distinguishing properties of the few protein families, including immunoglobulins, are revealed, based on the geometry of correlation matrices. We analyze the specific texture of these matrices, inherent to the specific families, and suggest a way to distinguish proteins from non-protein set of sequences.

The role of correlation matrix technique in classification is discussed. We suggest that the classification criteria should be based on the residues at the positions with the highest overall correlation with the other positions. Revealing the positions with various correlation strength helps to reconstruct the phylogeny of protein families. %A Omer Reingold %A Salil Vadhan %A Avi Wigderson %T Entropy Waves, the Zig-Zag Graph Product, and New Constant-Degree Expanders and Extractors %D February 23, 2001 %Z Thu, 5 Apr 2001 05:00:00 GMT %I DIMACS %R 2001-09 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-09.ps.gz %X

The main contribution of this work is a new type of graph product, which we call the \defword{zig-zag product}. Taking a product of a large graph with a small graph, the resulting graph inherits (roughly) its size from the large one, its degree from the small one, and its expansion properties from both! Iteration yields simple explicit constructions of constant-degree expanders of every size, starting from one constant-size expander.

Crucial to our intuition (and simple analysis) of the properties of this graph product is the view of expanders as functions which act as ``entropy wave'' propagators --- they transform probability distributions in which entropy is concentrated in one area to distributions where that concentration is dissipated. In these terms, the graph product affords the constructive interference of two such waves.

A variant of this product can be applied to extractors, giving the first explicit extractors whose seed length depends (poly)logarithmically on only the entropy deficiency of the source (rather than its length) and that extract almost all the entropy of high min-entropy sources. These high min-entropy extractors have several interesting applications, including the first constant-degree explicit expanders which beat the ``eigenvalue bound.'' %A Peter C. Fishburn %A Fred S. Roberts %T No-Hole L(2,1)-Colorings %D March 7, 2001 %Z Thu, 5 Apr 2001 05:00:00 GMT %I DIMACS %R 2001-10 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-10.ps.gz %X An L(2,1)-coloring of a graph G is a coloring of G's vertices with integers in {0,1, ..., k} so that adjacent vertices' colors differ by at least two and colors of distance-two vertices differ. We refer to an L(2,1)-coloring as a coloring. The span \lambda(G) of G is the smallest k for which G has a coloring, a span coloring is a coloring whose greatest color is \lambda (G), and the hole index \rho (G) of G is the minimum number of colors in {0,1, ..., \lambda (G) } not used in a span coloring. We say that G is full-colorable if \rho (G) =0. More generally, a coloring of G is a no-hole coloring if it uses all colors between 0 and its maximum color. Both colorings and no-hole colorings were motivated by channel assignment problems. We define the no-hole span \mu (G) of G as \infty if G has no no-hole coloring; otherwise \mu (G) is the minimum k for which G has a no-hole coloring using colors in {0,1, ..., k}. We prove that G is full-colorable if it has \lambda (G) +1 vertices. In addition, if G is not full-colorable and if it has at least \lambda (G) +2 vertices, then \mu (G) \le \lambda (G) + \rho (G). Moreover, for each m >= 1 there is a graph with \rho (G) = m and \mu (G) = \lambda (G) + \rho (G). %A Vince Grolmusz %A Benny Sudakov %T k-wise Set-Intersections and k-wise Hamming-Distances %D March 7, 2001 %Z Thu, 5 Apr 2001 05:00:00 GMT %I DIMACS %R 2001-11 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-11.ps.gz %X We prove a version of the Ray-Chaudhuri--Wilson and Frankl-Wilson theorems for $k$-wise intersections and also generalize a classical code-theoretic result of Delsarte for $k$-wise Hamming distances. A set of code-words $a^1,a^2,\ldots,a^k$ of length $n$ have $k$-wise Hamming-distance $\ell$, if there are exactly $\ell$ such coordinates, where not all of their coordinates coincide (alternatively, exactly $n-\ell$ of their coordinates are the same). We show a Delsarte-like upper bound: codes with few $k$-wise Hamming-distances must contain few code-words. %A Endre Boros %A Khaled Elbassioni %A Vladimir Gurvich %A Leonid Khachiyan %A Kazuhisa Makino %T Dual-Bounded Generating Problems: All Minimal Integer Solutions for a Monotone System of Linear Inequalities %D April 10, 2001 %Z Thu, 16 Aug 2001 09:00:00 GMT %I DIMACS %R 2001-12 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-12.ps.gz %X We consider the problem of enumerating all minimal integer solutions of a monotone system of linear inequalities. We first show that for any monotone system of $r$ linear inequalities in $n$ variables, the number of maximal infeasible integer vectors is at most $rn$ times the number of minimal integer solutions to the system. This bound is accurate up to a $polylog(r)$ factor and leads to a polynomial-time reduction of the enumeration problem to a natural generalization of the well-known dualization problem for hypergraphs, in which dual pairs of hypergraphs are replaced by dual collections of integer vectors in a box. We provide a quasi-polynomial algorithm for the latter dualization problem. These results imply, in particular, that the problem of incrementally generating all minimal integer solutions to a monotone system of linear inequalities can be done in quasi-polynomial time. %A Daniel Kral %A Jana Maxova %A Pavel Podbrdsky %A Robert Samal %T On Hamiltonian Cycles in Strong Products of Graphs %D April 11, 2001 %Z Thu, 16 Aug 2001 09:00:00 GMT %I DIMACS %R 2001-13 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-13.ps.gz %X

We prove that the strong product $G_1\times\cdots\times G_n$ contains a hamiltonian cycle for $n\ge\Delta$ whenever all $G_i$ are connected graphs of maximum degree at most $\Delta$; in particular $G^{\Delta(G)}$ contains a hamiltonian cycle. For large $\Delta$ we prove the same statement for $n\approx c\Delta$ for any $c>\ln (25/12) +1/60$.

The research was done as a part of Research Experience for Undergraduates programme; this is a joint programme of DIMACS at Rutgers University and DIMATIA at Charles University. The REU supervisors were J\'anos Koml\'os and Endre Szemer\'edi from Rutgers and Jan Kratochv\'{\i}l and Jaroslav Ne\v{s}et\v{r}il from Charles University. %A Endre Boros %A Khaled Elbassioni %A Vladimir Gurvich %A Leonid Khachiyan %T An inequality for polymatroid functions and its applications %D April 12, 2001 %Z Thu, 16 Aug 2001 09:00:00 GMT %I DIMACS %R 2001-14 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-14.ps.gz %X

An integral-valued set function $f:2^V \mapsto \ZZ$ is called polymatroid if it is submodular, non-decreasing, and $f(\emptyset)=0$. Given a polymatroid function $f$ and an integer threshold $t\geq 1$, let $\alpha=\alpha(f,t)$ denote the number of maximal sets $X \subseteq V$ satisfying $f(X) < t$, let $\beta=\beta(f,t)$ be the number of minimal sets $X \subseteq V $ for which $f(X) \ge t$, and let $n=|V|$. We show that if $\beta \ge 2$ then $\alpha \le \beta^{(\log t)/c}$, where $c=c(n,\beta)$ is the unique positive root of the equation $1=2^c(n^{c/\log\beta}-1)$. In particular, our bound implies that $\alpha \le (n\beta)^{\log t}$ for all $\beta \ge 1$. We also give examples of polymatroid functions with arbitrarily large $t, n, \alpha$ and $\beta$ for which $\alpha \ge \beta^{(.551 \log t)/c}$.

More generally, given a polymatroid function $f:2^V \mapsto \ZZ$ and an integral threshold $t \ge 1$, consider an arbitrary hypergraph $\cH$ such that $|\cH| \ge 2$ and $f(H) \ge t$ for all $H \in \cH$. Let $\cS$ be the family of all maximal independent sets $X$ of $\cH$ for which $f(X) < t$. Then $|\cS| \leq |\cH|^{(\log t)/c(n,|\cH|)}$. As an application, we show that given a system of polymatroid inequalities $f_1(X) \ge t_1,\ldots,f_m(X) \ge t_m$ with quasi-polynomially bounded right hand sides $t_1,\ldots,t_m$, all minimal feasible solutions to this system can be generated in incremental quasi-polynomial time. In contrast to this result, the generation of all maximal infeasible sets is an NP-hard problem for many polymatroid inequalities of small range. %A Juan Garay %A Joseph (Seffi) Naor %A B\"ulent Yener %A Peng Zhao %T On-line Admission Control and Job Scheduling with Preemption %D April 20, 2001 %Z Thu, 16 Aug 2001 09:00:00 GMT %I DIMACS %R 2001-15 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-15.ps.gz %X This paper studies the effect of preemption on the throughput of a single ``communication channel'' where requests arrive with a given processing time and slack. The problem is to decide which requests to serve so as to maximize the channel's utilization. This simple model captures many situations, both at the application (e.g., delivery of video) as well as at the network/transmission levels (e.g., scheduling of jobs at a switch). The problem is on-line in nature, and thus we use competitive analysis for measuring the performance of our scheduling algorithms. We consider two modes of operation: with and without commitment, and derive upper and lower bounds for each case. Since the competitive analysis is based on the worst-case scenario, the average-case performance of the on-line algorithms are examined by a simulation study. %A Olga Ourioupina %A Boris Galitsky %T Application of default reasoning to semantic processing under %D April 25, 2001 %Z Thu, 16 Aug 2001 09:00:00 GMT %I DIMACS %R 2001-16 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-16.ps.gz %X

We build the natural language question-answering system, where the query representation formula is subject to transformation in accordance to the set of default rules. This transformation is required to disambiguate entities in a vertical domain, where they usually have a principle meaning and a set of foreign ones. Default reasoning is discussed to be applicable to a variety of semantic processing algorithms, including the semantic header approach. Using default rules can be referred as pragmatic machinery, complementary to syntactic and semantic processing of complex queries in a vertical domain. The methodology of building the set of default rules is developed, capable of adding the essential entities or eliminating misleading ones to the representation of input query.

Implementation of operational semantics for default reasoning is suggested to transform the query representation by means of conflicting default rules. Technique of the keyword-based question answering is developed, where default rules link the set of potential queries with the initially coded canonical ones. The task of automatic annotation is then posed as building the set of keywords semantic headers and the set of canonical semantic headers for an answer.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-16.ps.gz %A Dean H. Lorenz %A Ariel Orda %A Danny Raz %A Yuval Shavitt %T How good can IP routing be? %D April 26, 2001 %Z Thu, 16 Aug 2001 09:00:00 GMT %I DIMACS %R 2001-17 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-17.ps.gz %X

In the traditional IP scheme, both the packet forwarding and the routing protocols are source invariant, i.e., their decisions depend on the destination IP address and not on the source address. Recent protocols, such as MPLS, as well as traditional circuit based protocols like PNNI allow routing decisions to depend both on the source and destination addresses. In fact, much of the theoretical work on routing assumes per-flow forwarding and routing, i.e., the forwarding decision is based both on the source and destination addresses.

The benefit of per-flow forwarding is well-accepted, so is the practical implications of its deployment. Nevertheless, no quantitative study has been carried on the performance differences between the two approaches.

This work aims at investigating the toll in terms of performance degradation that is incurred by source invariant schemes, as opposed to the per-flow alternatives. We show, both theoretically and by simulations, that source invariant routing can be significantly worse than per-flow routing. Realizing that static shortest path algorithms are not optimal even among the source invariant routing algorithms, we develop novel routing algorithms that are based on dynamic weights, and empirically study their performance in an Internet like environment.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-17.ps.gz %A Shuhong Gao %A D. Frank Hsu %T Short containers in Cayley graphs %D May 8, 2001 %Z Thu, 16 Aug 2001 09:00:00 GMT %I DIMACS %R 2001-18 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-18.ps.gz %X The star diameter of a graph measures the minimum distance from any source node to several other target nodes in the graph. For a class of Cayley graphs from abelian groups, a good upper bound for their star diameters is given in terms of the usual diameters and the orders of elements in the generating subsets. This bound is tight for several classes of graphs including hypercubes and directed $n$-dimensional tori. The technique used is the so-called disjoint ordering for a system of subsets, due to Gao, Novick and Qiu (1998). %A Philip MacKenzie %A Michael K. Reiter %T Networked Cryptographic Devices Resilient to Capture %D May 10, 2001 %Z Thu, 16 Aug 2001 09:00:00 GMT %I DIMACS %R 2001-19 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-19.ps.gz %X We present a simple technique by which a device that performs private key operations (signatures or decryptions) in networked applications, and whose local private key is activated with a password or PIN, can be immunized to offline dictionary attacks in case the device is captured. Our techniques do not assume tamper resistance of the device, but rather exploit the networked nature of the device, in that the device's private key operations are performed using a simple interaction with a remote server. This server, however, is untrusted---its compromise does not reduce the security of the device's private key unless the device is also captured---and need not have a prior relationship with the device. We further extend this approach with support for "key disabling", by which the rightful owner of a stolen device can disable the device's private key even if the attacker already knows the user's password. %A Rahul Shah %A Ravi Jain %A S. Rajagopalan %A Farooq Anjum %T Mobile Filters for Efficient Dissemination of Personalized Information Using Content-Based Multicast %D June 16, 2001 %Z Thu, 16 Aug 2001 09:00:00 GMT %I DIMACS %R 2001-20 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-20.ps.gz %X There has been a surge of interest in the delivery of personalized information to users (e.g. personalized stocks or travel information), particularly as the amount of information readily available from sources like the World Wide Web increases, and mobile users with limited terminal device capabilities increasingly desire updated, targeted information in real time. When the number of information recipients is large and there is sufficient commonality in their interests, as is often the case, it is worthwhile to use multicast rather than unicast to deliver the information. However, traditional multicast services, e.g. at the IP level, do not consider the structure and semantics of the information in the multicast process. We consider the use of Content-Based Multicast (CBM) where extra content filtering is performed at the interior nodes of the multicast tree so as to reduce network bandwidth usage and delivery delay, as well as to reduce the computation required at the sources and sinks. Note that filtering could be performed at the IP level or, more likely, at higher software layers e.g. in applications such as publish-subscribe and event notification systems.

In this paper we evaluate the situations in which CBM is worthwhile. The benefits of CBM depend critically upon how well filters are placed at interior nodes of the multicast tree, and the costs depend upon those introduced by filters themselves. Further, we consider the benefits of allowing the filters to be mobile so as to respond to user mobility or changes in user interests, and the corresponding costs of filter mobility. We consider two criteria: minimizing total network bandwidth utilization and minimizing mean information delivery delay. For each criterion we also develop a heuristic that runs faster than the optimal algorithm. Finally, we evaluate all the algorithms by means of simulation experiments.

Our results indicate that filters can be effective in substantially reducing bandwidth and delay. We also find filter mobility is worthwhile if there is sufficient locality in the interests of users, or there is marked large-scale user mobility. We conclude with suggestions for further work. %A Richard Lyons %T Generalized Fitting Subgroups and p-Layers of Finite Groups %D June 21, 2001 %Z Thu, 16 Aug 2001 09:00:00 GMT %I DIMACS %R 2001-21 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-21.ps.gz %X The similarities between Bender's generalized Fitting subgroup, Bender's E(G) subgroup and the Gorenstein-Walter $p$-layer of a finite group are axiomatized. %A Alair Pereira do Lago %T Local Groups in Free Burnside Groupoids %D June 26, 2001 %Z Thu, 16 Aug 2001 09:00:00 GMT %I DIMACS %R 2001-22 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-22.ps.gz %X

The study of repeated sequences is the basis of the study of \fb{groups} and \fb{semigroups}, and a better knowledge on Burnside algebras can be very useful in the analysis of many properties of sequences containing repetitions. The main theorem announced here establishes an important connection between \fb{groups} and \fb{semigroups}. In order to establish this connection, we use interesting properties on graphs, categories, combinatorics on words to obtain the algebraic main theorem.

Let $\grafo{G}$ be~a (possibly infinite) strongly connected graph and let $\T$ be a set of monoid identities such that any monoid satisfying $\T$ is also a group. Let $\cat{B}$ be~the free groupoid on $\grafo{G}$ satisfying $\T$. Then, the local groups $\local{B}{v}$, for $v\in \vertices{G}$, are all isomorphic to a free group satisfying $\T$. Furthermore, it is free over a generating set which can be effectively characterized and whose cardinality is the cyclomatic number of the graph $\grafo{G}$. %A Amr Elmasry %T Generalized Pairing Heaps %D July 31, 2001 %Z Thu, 16 Aug 2001 09:00:00 GMT %I DIMACS %R 2001-23 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-23.ps.gz %X We give a generalized form for the standard implementation of the pairing heaps. A new parameter k is introduced. When the node with the minimum value is to be deleted from the heap, the operations to combine the resulting sub-trees into one tree depend on the value of k. When the value of k is equal to 2, the implementation will be equivalent to the standard pairing heaps' implementation. We show that, for any constant k, this general form achieves the same bounds as the standard implementation. Finally, experimental results are conducted showing that, by tuning the value of k, the number of comparisons involved in this operation can be reduced. %A Amr Elmasry %T Optimal Adaptive Sorting %D July 31, 2001 %Z Thu, 16 Aug 2001 09:00:00 GMT %I DIMACS %R 2001-24 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-24.ps.gz %X We introduce Binomialsort, an adaptive sorting algorithm that is optimal with respect to the number of inversions. The number of comparisons performed by Binomialsort, on an input sequence of length n that has I inversions, is at most $2n \log{\frac{I}{n}} + O(n)$. The bound on the number of comparisons is further reduced to $\frac{3}{\log{3}} n \log{\frac{I}{n}} + O(n)$ by using a new structure, which we call trinomial queues. Experimental results show that our sorting algorithm is practical, efficient and easy to implement. %A Amir Dembo %A Abram Kagan %A Lawrence A. Shepp %T Remarks on the maximum correlation coefficient %D August 15, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-25 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-25.ps.gz %X The maximum correlation coefficient between partial sums of independent identically distributed random variables with finite second moment equals the classical (Pearson) correlation coefficient between the sums and, thus, does not depend on the distribution of the random variables. Besides proving this, relations between linearity of regression of each of two random variables on the other and the maximum correlation coefficient are discussed. %A Graham Cormode %A S. Muthukrishnan %T The String Edit Distance Matching Problem with Moves %D August 15, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-26 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-26.ps.gz %X

The edit distance between two strings S and R is defined to be the minimum number of character inserts, deletes and changes needed to convert R to S. Given a text string t of length n, and a pattern string p of length m, informally, the string edit distance matching problem is to compute the smallest edit distance between p and substrings of t. A well known dynamic programming algorithm takes time O(nm) to solve this problem, and it is an important open problem in Combinatorial Pattern Matching to significantly improve this bound.

We relax the problem so that (a) we allow an additional operation, namely, substring moves, and (b) we approximate the string edit distance upto a factor of O(log n log* n).(log*n is the number of times log function is applied to n to produce a constant.) Our result is a neat linear time deterministic algorithm for this version of the problem. This is the first known significantly subquadratic algorithm for a string edit distance problem in which the distance involves nontrivial alignments. Our results are obtained by embedding strings into L_1 vector space using a simplified parsing technique we call Edit Sensitive Parsing (ESP). This embedding is approximately distance preserving, and we show many applications of this embedding to string proximity problems including nearest neighbors, outliers, and streaming computations with strings. %A Vincent Mousseau %A Luis Dias %T Fuzzy outranking relations in ELECTRE providing manageable disaggregation procedures %D August 15, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-27 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-27.ps.gz %X

In ELECTRE methods, the construction of an outranking relation $S$ amounts at validating or invalidating, for any pair of alternatives $(a,b) \in A$, an assertion $aSb$. This comparison is grounded on the evaluation vectors of both alternatives, and on additional information concerning the DM's preferences, accounting for two conditions: concordance and non-discordance.

In decision processes using these methods, the analyst should interact with DM(s) in order to elicit values for preferential parameters. This can be done either directly or through a disaggregation procedure that infers the parameters values from holistic judgements provided by the DM(s). Inference is usually performed through an optimization program that accounts for the aggregation model and minimizes an ``error function". Although disaggregation approaches have been largely used in additive models, only few advances have been made towards a disaggregation approach for ELECTRE methods. This probably reflects the ``optimization unfriendly" character of the most recent ELECTRE methods.

In this paper we are concerned with a slight adaptation of the fuzzy outranking relation used in the ELECTRE III and ELECTRE TRI that preserves the original ideas and is more optimization-friendly for parameter inference programs. Such modification is shown to preserve the original discordance concept. We show that the modified outranking relation makes it easier to solve inference programs. %A Linchun Gao %A Andras Prekopa %T On Performance Prediction of Cellular Telephone Networks %D August 29, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-28 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-28.ps.gz %X This paper considers large cellular mobile networks in which the arrival rates of calls for different cells are different. The lower and upper bound of how much the given number of channels would satisfy the arriving calls are presented. Numerical examples are given. %A Amr Elmasry %T Adaptive Properties of Pairing Heaps %D September 14, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-29 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-29.ps.gz %X We show that the pairing heap benefits from the presortedness in the input sequence, and sorts adaptively. In particular, we show that given an input sequence of size $n$ that is already sorted in ascending order from right to left, repeatedly deleting the smallest element, using the pairing heap operation, requires at most $7n$ comparisons. We also show that starting with any initial heap structure that has the property that the corresponding sequence of the heap is sorted in ascending order, at most $7n$ comparisons are required to produce the sorted sequence by repeatedly deleting the smallest element from the heap. This latter result implies an easy proof for Tarjan's sequential access theorem for splay trees, with a better bound of $3.5n$ rotations. Finally, experimental results are conducted, supporting the fact that the pairing heap is adaptive by comparing sorting using the pairing heap with Splaysort and Binomialsort. %A Amr Elmasry %T Scrambled pairing and square-root trees %D September 14, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-30 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-30.ps.gz %X

An n-node forest of trees is called a square-root forest, if it has the following structure. For a given positive integer $k$ the forest has $2k$ trees. The first $k+1$ are single nodes. For the other $k-1$ trees, the root of tree $l$ has $l$ single-node children, for all $l$ from 1 to $k-1 $. If $n \neq k+\frac{k \; (k+1)}{2}$ the definition is slightly different.

Given a forest of $\tau$ trees, the rank of a tree is defined to be the number of children of the root of this tree. A phase of operations is defined as first linking the trees in pairs, then replacing the tree with the largest rank with its sub-trees together with a new single-node tree. The pairing is done by first sorting the trees by rank and numbering them from $1$ to $\tau$, then linking the root of tree $l$ to the root of tree $l+\lceil \tau/2 \rceil$, for all $l$ from $1$ to $\lfloor \tau/2 \rfloor$. We give a combinatorial proof that after applying an $O(n^{1.5})$ phases, the forest will converge to the square-root forest.

It is proven in \cite{fsst} that using any pairing strategy, the amortized cost of deleting the item with the minimum value from a heap is $O(\sqrt{n})$. Our pairing strategy gives $\Theta(\sqrt{n})$ amortized cost for this operation. %A B. Derrida %A J. L. Lebowitz %A E. R. Speer %T Large Deviation of the Density Profile in the Symmetric Simple Exclusion Process %D September 20, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-31 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-31.ps.gz %X We consider an open one dimensional lattice gas on sites $i=1,\dots,N$, with particles jumping independently with rate $1$ to neighboring interior empty sites, the {\it simple symmetric exclusion process}. The particle fluxes at the left and right boundaries, corresponding to exchanges with reservoirs at different chemical potentials, create a stationary nonequilibrium state (SNS) with a steady flux of particles through the system. The mean density profile in this state, which is linear, describes the typical behavior of a macroscopic system, i.e., this profile occurs with probability 1 when $N \to \infty$. The probability of microscopic configurations corresponding to some other profile $\rho(x)$, $x = i/N$, has the asymptotic form $\exp[-N {\cal F}(\{\rho\})]$; $\cal F$ is the {\it large deviation functional}. In contrast to equilibrium systems, for which ${\cal F}_{eq}(\{\rho\})$ is just the integral of the appropriately normalized local free energy density, the $\cal F$ we find here for the nonequilibrium system is a nonlocal function of $\rho$. This gives rise to the long range correlations in the SNS predicted by fluctuating hydrodynamics and suggests similar non-local behavior of $\cal F$ in general SNS, where the long range correlations have been observed experimentally. %A Endre Boros %A Robert E. Jamison %A Renu Laskar %A Henry Martyn Mulder %T On 3-Simplicial Vertices in Planar Graphs %D September 24, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-32 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-32.ps.gz %X A vertex $v$ in a graph $G = (V,E)$ is {\em $k$-simplicial} if the neighborhood $N(v)$ of $v$ can be vertex-covered by $k$ or fewer complete graphs. The main result of the paper states that a planar graph of order at least four has at least four 3-simplicial vertices of degree at most five. This result is a strengthening of the classical corollary of Euler's Formula that a planar graph of order at least four contains at least four vertices of degree at most five. %A Endre Boros %A Peter L. Hammer %T Pseudo-Boolean Optimization %D September 24, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-33 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-33.ps.gz %X This survey examines the state of the art of a variety of problems related to pseudo-Boolean optimization, i.e. to the optimization of set functions represented by closed algebraic expressions. The main parts of the survey examine general pseudo-Boolean optimization, the specially important case of quadratic pseudo-Boolean optimization (to which every pseudo-Boolean optimization can be reduced), several other important special classes, and approximation algorithms. %A Bela Csaba %A Sachin Lodha %T A Randomized Online Algorithm for the k-Server Problem on a Line %D October 1, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-34 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-34.ps.gz %X We give a $O(n^{2 \over 3}\log{n})$-competitive randomized $k$--server algorithm when the underlying metric space is given by $n$ equally spaced points on a line. For $n = k + o(k^{3 \over 2}/\log{k})$, this algorithm is $o(k)$--competitive. %A Giovanni Di Crescenzo %A Clemente Galdi %T Secret Sharing and Hypergraph Decomposition %D November 1, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-35 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-35.ps.gz %X

A secret sharing scheme is a protocol by which a dealer distributes a secret among a set of participants in such a way that only qualified sets of them can reconstruct the value of the secret whereas any non-qualified subset of participants obtain no information at all about the value of the secret. Secret sharing schemes have always played a very important role in the construction of higher level cryptographic primitives and protocols.

In this paper we investigate the construction of efficient secret sharing schemes by using a technique called {\em hypergraph decomposition}, extending in a non-trivial way the previously studied graph decomposition technique.

The application of this technique allows us to obtain secret sharing schemes for particular and large classes of access structures (such as hyperpaths, hypercycles, hyperstar and hypertrees) with dramatically improved efficiency over previous results. Specifically, in all cases, schemes obtained using previous techniques generate shares of exponential blowup in size, while for ours the blowup is always polynomial, in some cases even constant. Our schemes are also complemented by bounds on the blowup that are essentially tight.

In the course of the formulation of the hypergraph decomposition technique, we also obtain an elementary characterization of the ideal access structures among the hyperstar, which is of independent interest. %A Ali Shokoufandeh %A Yi Zhao %T On a Tiling Conjecture of Komlos for 3-Chromatic Graphs %D November 1, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-36 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-35.ps.gz %X Given two graphs $G$ and $H$, an $H$-{\em matching} of $G$ (or a {\em tiling} of $G$ with $H$) is a subgraph of $G$ consisting of vertex-disjoint copies of $H$. For an $r$-chromatic graph $H$ on $h$ vertices, we write $u=u(H)$ for the smallest possible color-class size in any $r$-coloring of $H$. The {\em critical chromatic number} of $H$ is the number $\chi_{cr}(H)=(r-1)h/(h-u)$. A conjecture of Koml\'{o}s states that for every graph $H$, there is a constant $K$ such that if $G$ is any $n$-vertex graph of minimum degree at least $\left(1-(1/\chi_{cr}(H))\right)n$, then $G$ contains an $H$-matching that covers all but $K$ vertices of $G$. In this paper we prove that the conjecture holds for all sufficiently large values of $n$, when $H$ is a 3-chromatic graph. %A Philip MacKenzie %A Michael K. Reiter %T Delegation of Cryptographic Servers for Capture-Resilient Devices %D November 1, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-37 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-37.ps.gz %X A device that performs private key operations (signatures or decryptions), and whose private key operations are protected by a password, can be immunized against offline dictionary attacks in case of capture by forcing the device to confirm a password guess with a designated remote server in order to perform a private key operation. Recent proposals for achieving this allow untrusted servers and require no server initialization per device. In this paper we extend these proposals to enable dynamic delegation from one server to another; i.e., the device can subsequently use the second server to secure its private key operations. One application is to allow a user who is traveling to a foreign country to temporarily delegate to a server local to that country the ability to confirm password guesses and aid the user's device in performing private key operations, or in the limit, to temporarily delegate this ability to a token in the user's possession. Another application is proactive security for the device's private key, i.e., proactive updates to the device and servers to eliminate any threat of offline password guessing attacks due to previously compromised servers. %A Yi Zhao %T On a Conjecture of Loebl %D November 1, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-38 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-38.ps.gz %X Martin Loebl conjectured that if in a graph $G$ on $n$ vertices at least half the vertices have degree at least $n/2$, then $G$ contains, as subgraphs, all trees with at most $n/2$ edges. We prove the conjecture for sufficient large $n$. %A I. E. Zverovich %T Extended $(P_5, {\overline P_5})$-free graph %D November 1, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-39 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-39.ps.gz %X Let $G$ and $H$ be graphs. A {\em substitution} of $H$ in $G$ instead of a vertex $v \in V(G)$ is the graph $G(v \to H)$, which consists of disjoint union of $H$ and $G - v$ with the additional edge-set $\{xy: x \in V(H), y \in N_G(v)\}$.

For a hereditary class of graphs ${\mathcal P}$, the {\em substitutional closure} of ${\mathcal P}$ is defined as the class ${\mathcal P}^*$ consisting of all graphs which can be obtained from graphs in $P$ by repeated substitutions.

We characterize the substitutional closure $(P_5 \cup K_1, {\overline P_5} \cup K_1)$-free graphs in terms of forbidden induced subgraphs.

The weighted stability problem is polynomially solvable for this class. %A I. E. Zverovich %T Characterization of superbipartite graphs %D November 1, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 20 01-40 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-40.ps.gz %X Let $G$ and $H$ be graphs. A {\em substitution} of $H$ in $G$ instead of a vertex $v \in V(G)$ is the graph $G(v \to H)$, which consists of disjoint union of $H$ and $G - v$ with the additional edge-set $\{xy: x \in V(H), y \in N_G(v)\}$.

For a hereditary class of graphs ${\mathcal P}$, the {\em substitutional closure} of ${\mathcal P}$ is defined as the class ${\mathcal P}^*$ consisting of all graphs which can be obtained from graphs in $P$ by repeated substitutions.

Let ${\mathcal B}$ be the class of all graphs $G$ such that $G - N[v]$ is a bipartite graph for every vertex $v$ of $G$. Here $N[v]$ denotes the closed neighborhood of $v$. A graph is called a {\em superbipartite graph} if it is in the substitutional closure of ${\mathcal B}$.

We characterize superbipartite graphs in terms of forbidden induced subgraphs. Note that the weighted stability number in ${\mathcal B}^*$ can be found in polynomial time. %A Piotr Berman %A Sridhar Hannenhalli %A Marek Karpinski %T 1.375-Approximation Algorithm for Sorting by Reversals %D November 7, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-41 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-41.ps.gz %X Analysis of genomes evolving by inversions leads to a general combinatorial problem of {\em Sorting by Reversals}, MIN-SBR, the problem of sorting a permutation by a minimum number of reversals. This combinatorial problem has a long history, and a number of other motivations. It was studied in a great detail recently in computational molecular biology. Following a series of preliminary results, Hannenhalli and Pevzner developed the first exact polynomial time algorithm for the problem of sorting signed permutations by reversals, and a polynomial time algorithm for a special case of unsigned permutations. The best known approximation algorithm for MIN-SBR, due to Christie, gives a performance ratio of 1.5. In this paper, by exploiting the polynomial time algorithm for sorting signed permutations and by developing a new approximationalgorithm for maximum cycle decomposition of breakpoint graphs, we improve the performance ratio for MIN-SBR to 1.375. Besides its biological and combinatorial importance, better approximation algorithms for MIN-SBR have become particularly challenging recently because this problem has been proven to NP-hard by Caprara, and MAX-SNP hard by Berman and Karpinski, excluding thus an existence of a polynomial time approximation scheme (PTAS) for that problem. %A Piotr Berman %A Marek Karpinski %T Efficient Amplifiers and Bounded Degree Optimization %D November 7, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-42 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-42.ps.gz %X This paper studies the existence of efficient (small size) amplifiers for proving explicit inaproximability results for bounded degree and bounded occurrence combinatorial optimization problems, and gives an explicit construction for such amplifiers. We use this construction also later to improve the currently best known approximation lower bounds for bounded occurrence instances of linear equations mod 2, and for bounded degree (regular) instances of MAX-CUT. In particular we prove the approximation lower bound of 152/151 for exactly 3-occurrence E3-OCC-E2-LIN-2 problem, and MAX-CUT problem on 3-regular graphs, E3-MAX-CUT, and the approximation lower bound of 121/120 for E3-OCC-2-LIN-2 problem. As an application we are able to improve also the best known approximation lower bound for E3-OCC-MAX-E2SAT. %A Anna C. Gilbert %A Yannis Kotidis %A S. Muthukrishnan %A Martin. J. Strauss %T QuickSAND: Quick Summary and Analysis of Network Data %D November 8, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-43 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-43.ps.gz %X Monitoring and analyzing traffic data generated from large ISP networks imposes challenges both at the data gathering phase as well as the data analysis itself. Still, both tasks are crucial for responding to day to day challenges of engineering large networks with thousands of customers. In this paper we build on the premise that approximation is a necessary evil of handling massive datasets such as network data. We propose building compact summaries of the traffic data called sketches at distributed network elements and centers. These sketches are able to respond well to queries that seek features that stand out of the data. We call such features ``heavy hitters.'' In this paper, we describe sketches and show how to use sketches to answer aggregate and trend-related queries and identify heavy hitters. This may be used for exploratory data analysis of network operations interest. We support our proposal by experimentally studying AT&T WorldNet data and performing a feasibility study on the Cisco NetFlow data collected at several routers. %A Anna C. Gilbert %A Sudipto Guha %A Piotr Indyk %A S. Muthukrishnan %A Martin J. Strauss %T Near-Optimal Sparse Fourier Representations via Sampling %D November 15, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-44 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-44.ps.gz %X We give an algorithm for finding a Fourier representation r of B terms for a given discrete signal a of length N, such that the sum-square error is within the factor (1+ epsilon) of best possible sum-square error. Our algorithm can access the signal a by reading its values on a sample set T, chosen randomly from a (non-product) distribution of our choice, independent of the signal a. That is, we sample non-adaptively. The total time cost of the algorithm is polynomial in B log(N) log(M)/epsilon (where M is a standard input precision parameter), which implies a similar bound for the number of samples. %A Dragan Stevanovic %T On the components of NEPS of connected bipartite graphs %D November 20, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-45 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-45.ps.gz %X

Back in 1983, D.~Cvetkovi\'c posed the conjecture that the components of NEPS of connected bipartite graphs are almost cospectral. In 2000, we showed that this conjecture does not hold for infinitely many bases of NEPS, and we posed a necessary condition on the base of NEPS for NEPS to have almost cospectral components. At the same time, D.~Cvetkovi\'c posed weaker version of his original conjecture which claims that each eigenvalue of NEPS is also the eigenvalue of each component of NEPS.

Here we prove this weaker conjecture, give an upper bound on the multiplicity of an eigenvalue of NEPS as an eigenvalue of its component, give new sufficient condition for the almost cospectrality of components of NEPS of connected bipartite graphs, and characterize the bases of NEPS which satisfy this condition. %A Dragan Stevanovic %T Antipodal graphs of small diameter %D November 27, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-46 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-46.ps.gz %X

A proper metric space $X=(X,d)$ is called {\em antipodal} if -- with $[x,y]=\{z\in X\,\colon\,d(x,y)=d(x,z)+d(z,y)\}$ -- for every $x\in X$ there exists some $y\in X$ such that $[x,y]=X$. A connected undirected finite graph~$G$ is called {\em antipodal} if its associated graph metric is antipodal.

Here we characterize antipodal graphs of diameter~$3$ and show that almost every graph is an induced subgraph of some antipodal graph of diameter~$3$. %A Pierre Hansen %A Hadrien Melot %A Dragan Stevanovic %T Integral Complete Split Graphs %D November 27, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-47 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-47.ps.gz %X We give characterizations of integral graphs in the family of complete split graphs and a few related families of graphs. %A Dragan Stevanovic %A Gilles Caporossi %T On the separator of fullerenes %D December 7, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-48 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-48.ps.gz %X The separator of a graph is the difference between the two largest eigenvalues of its adjacency matrix. The program {\em Graffiti}, developed by S.~Fajtlowicz, posed the conjecture that the separator of any fullerene is at most~$1$. Here we prove this conjecture by using the {\it interlacing theorem} in an interesting manner and then extend this method to show that the dodecahedron has the largest separator amongst all fullerenes. %A Srikrishnan Divakaran %A Michel Saks %T Approximation algorithms for Offline scheduling with set-ups %D December 21, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-49 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-49.ps.gz %X In this paper, we present new approximation results for the offline problem of scheduling $n$ independent jobs with sequence independent set-ups and common release times on a single machine system for the following optimality criteria :

- total weighted completion time

- maximum lateness

For the total weighted completion time criterion, we present a $2$-approximation algorithm, the first known polynomial time constant approximation algorithm for this problem. For this criterion, when the number of job types is arbitrary, the computational complexity is open and prior to our results there were no known polynomial time constant approximation algorithms even when all jobs have unit weight and all job types have unit set-up times.

For the maximum lateness criterion, we present an algorithm that obtains an optimal solution in a relaxed framework where our algorithm is given strictly more resources (i.e. a machine with higher processing speed) than the optimal offline algorithm to which it is compared. For this criterion, when the number of job types is arbitrary, this problem is known to be $NP$-hard even when there are two jobs in each type or when all job types have unit set-up times, there are at most three jobs in each type and there are at most three distinct due dates. Also, for this criterion, when the number of job types and the due dates are arbitrary, there are no constant approximation algorithms unless $P=NP$. %A Srikrishnan Divakaran %A Michel Saks %T Online scheduling with release times and set-ups %D December 21, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-50 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-50.ps.gz %X In this paper, we address the problem of online scheduling of $n$ independent jobs with release times and sequence independent set-ups on a single machine system with the objective of minimizing the maximum flow time. For this problem, we present an $O(1)$-competitive online algorithm. We also present the proof of $NP$-completeness of the offline problem. %A Ali Shokoufandeh %A Yi Zhao %T Proof of a Tiling Conjecture of Komlos %D December 21, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-51 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-51.ps.gz %X Given two graphs $G$ and $H$, an $H$-{\em matching} of $G$ (or a {\em tiling} of $G$ with $H$) is a subgraph of $G$ consisting of vertex-disjoint copies of $H$. For an $r$-chromatic graph $H$ on $h$ vertices, we write $u=u(H)$ for the smallest possible color-class size in any $r$-coloring of $H$. The {\em critical chromatic number} of $H$ is the number $\chi_{cr}(H)=(r-1)h/(h-u)$. A conjecture of Koml\'{o}s states that for every graph $H$, there is a constant $K$ such that if $G$ is any $n$-vertex graph of minimum degree at least $\left(1-(1/\chi_{cr}(H))\right)n$, then $G$ contains an $H$-matching that covers all but $K$ vertices of $G$. In this paper we prove that the conjecture holds for all sufficiently large values of $n$. %A A. Barg %A G. R. Blakley %A G. Kabatiansky %T Digital fingerprinting codes: Problems statements, constructions, identification of traitors %D November 21, 2001 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-52 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-52.ps.gz %X We consider a general fingerprinting problem of digital data under which coalitions of users can alter or erase some bits in their copies in order to create an illegal copy. Each user is assigned a fingerprint which is a word in a fingerprinting code of size M (the total number of users) and length n. We present binary fingerprinting codes secure against size-t coalitions which enable the distributor (decoder) to recover at least one of the users from the coalition with probability of error exp(-Omega(n)) for M=exp(Omega(n)). This is an improvement over the best known schemes that provide the error probability no better than exp(-Omega(n^{1/2})) and for this probability support at most exp(O(n^{1/2})) users. The construction complexity of codes is polynomial in n. We also present versions of these constructions that afford poly(n)=poly log(M) identification algorithms of a member of the coalition, improving over the best previously known complexity of Omega(M).

For the case t=2 we construct codes of exponential size with even stronger performance, namely, the distributor can either recover both users from the coalition with probability 1-exp(Omega(n)), or identifies one traitor with probability 1. %A I. E. Zverovich %T Weighted stability in hypergraphs and weighted domination in split graphs %D January 1, 2002 %Z Mon, 31 Dec 2001 09:00:00 GMT %I DIMACS %R 2001-53 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2001/2001-53.ps.gz %X We define a family of hereditary subclasses of split graphs where the weighted domination problem is polynomially solvable. Our approach is similar to that of Balas and Yu \cite{BalasY89} for maximal stable sets in graphs.

We apply the result to the subproblem of finding the weighted stability number of a hypergraph. %A Vince Grolmusz %T A Trade-Off for Covering the Off-Diagonal Elements of Matrices %D January 22, 2002 %Z Tue Apr 23 18:22:25 EDT 2002 %I DIMACS %R 2002-01 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-01.ps.gz %X We would like to cover all the off-diagonal elements of an $n\times n$ matrix by non-necessarily contiguous rectangular submatrices; the diagonal elements cannot be covered. It is not difficult to give a cover with $2\lceil \log n\rceil$ rectangles, where some off-diagonal elements are covered as many as $\lceil \log n\rceil$-times, or another cover, using $n$ rectangles and any off-diagonal elements of the matrix is covered only once. We show that one cannot attain {\it both} low covering multiplicity and a small number of covering rectangles at the same time: We prove a trade-off between these two numbers. %A D. Frank Hsu %A Xingde Jia %T Additive Bases and Extremal Problems in Groups, Graphs and Networks %D January 22, 2002 %Z Tue Apr 23 18:22:26 EDT 2002 %I DIMACS %R 2002-02 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-02.ps.gz %X Bases in sets and groups and their extremal problems have been studied in additive number theory such as the postage stamp problem. On the other hand, Cayley graphs based on specific finite groups have been studied in algebraic graph theory and applied to constant efficient communication networks such as circulant networks with minimum diameter (or transmission delay). In this paper we establish a framework which defines and unifies additive bases in groups, graphs and networks and survey results on the bases and their extremal problems. Some well known and well studied problems such as harmonious graphs and perfect addition sets are also shown to be special cases of the framework. %A Victoria Ungureanu %T Regulating E-Commerce through Contract Certificates %D January 25, 2002 %Z Tue Apr 23 18:22:26 EDT 2002 %I DIMACS %R 2002-03 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-03.ps.gz %X

Enforcing e-commerce contracts is difficult because an enterprise may be concurrently bound by a very large number of commercial agreements, and because these agreements are likely to change in time or to be annulled. We argue that it is not feasible to establish a dedicated server for each contract; nor it is possible to construct a composition of such commercial agreements. To deal with these problems we propose to embed contracts in certificates. We show that disseminating contracts as certificates facilitates deployment, annulment and revision of contracts. We propose a language for stating contract terms, and present several formal examples.

We describe here our implementation, which can be used as an extension to a web server, or as a separate server with interface to application. The proposed model does not require any modification of the current certificate infrastructure, and only minor modifications to servers. %A Melvin F. Janowitz %T The Controversy About Continuity of Clustering Algorithms %D February 5, 2002 %Z Tue Apr 23 18:22:27 EDT 2002 %I DIMACS %R 2002-04 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-04.ps.gz %X It is not meaningful to talk about continuous cluster algorithms for use with data having only ordinal significance. An ordinal version of continuity for such data is introduced and studied. %A Melvin F. Janowitz %T The split systems generated by a connected graph %D February 5, 2002 %Z Tue Apr 23 18:22:28 EDT 2002 %I DIMACS %R 2002-05 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-05.ps.gz %X The bridges of a connected graph G are shown to generate splits of G that are compatible in the sense that they generate a tree. The results are extended to generalized bridges, and the theory is applied to develop new clustering algorithms. These algorithms operate by removing at each level any bridges (or generalized bridges) from the threshold graph at that level before applying any clustering criterion. %A Zdenek Dvorak %A Jan Kara %A Daniel Kral %A Ondrej Pangrac %T On Pattern Coloring of Cycle Systems %D February 19, 2002 %Z Tue Apr 23 18:22:29 EDT 2002 %I DIMACS %R 2002-06 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-06.ps.gz %X

A k-cycle system is a system of cyclically ordered k-tuples of a finite set. A pattern is a sequence of letters. A coloring of a k-cycle system with respect to a set of patterns of length k is proper iff each cycle is colored consistently with one of the patterns, i.e. the same/distinct letters correspond to (the) same/distinct color(s). The feasible set of a cycle system is the set of all l's such that there exists a proper coloring of it using exactly l colors.

For all combinations of a pattern set P and a number l, we either find a polynomial algorithm or prove NP--completeness of the problem whether a given cycle system with a set of patterns P can be colored by at most l colors. We further construct a cycle system with a prescribed feasible set for almost every set of patterns containing only two different letters. %A Gary Gordon %T Expected rank in antimatroids %D February 21, 2002 %Z Tue Apr 23 18:22:30 EDT 2002 %I DIMACS %R 2002-07 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-07.ps.gz %X We consider a probabilistic antimatroid $A$ on the ground set $E$, where each element $e \in E$ may succeed with probability $p_e$. We focus on the expected rank $ER(A)$ of a subset of $E$ as a polynomial in the $p_e$. General formulas hold for arbitrary antimatroids, and simpler expressions are valid for certain well-studied classes, including trees, rooted trees, posets, and finite subsets of the plane. We connect the Tutte polynomial of an antimatroid to $ER(A)$. When $S$ is a finite subset of the plane with no three points collinear, we derive an expression for the expected rank which has surprising symmetry properties. Corollaries include new formulas involving the beta invariant of subsets of $S$ and new proofs of some known formulas. %A David Avis %A Vasek Chvatal %T On a conjecture of Baiou and Balinski %D March 14, 2002 %Z Tue Apr 23 18:22:31 EDT 2002 %I DIMACS %R 2002-08 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-08.ps.gz %X We disprove a conjecture of Baiou and Balinski concerning a variation on the Birkhoff-von Neumann theorem. %A Vince Grolmusz %T Pairs of Codes with Prescribed Hamming Distances and Coincidences %D March 21, 2002 %Z Tue Apr 23 18:22:31 EDT 2002 %I DIMACS %R 2002-09 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-09.ps.gz %X In this work we describe a fast algorithm for generating pairs of q-ary codes with prescribed pairwise Hamming-distances and coincidences (for a letter $s\in\{0,1,\ldots,q-1\}$, the number of $s$-coincidences between codewords $a$ and $b$ is the number of letters $s$ in the same positions both in $a$ and $b$). The method is a generalization of a method for constructing set-systems with prescribed intersection sizes (V. Grolmusz: Constructing Set-Systems with Prescribed Intersection Sizes, DIMACS Technical Report No. 2001-03), where only the case $q=2$ and $s=1$ was examined. We also generate codes with prescribed $k$-wise coincidences and Hamming-distances. %A Boris Galitsky %T Use of virtual semantic headers to improve the coverage of natural language question answering domains %D March 24, 2002 %Z Tue Apr 23 18:22:32 EDT 2002 %I DIMACS %R 2002-10 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-10.ps.gz %X We report on the knowledge representation mechanism designed for natural language question-answering system to function in such poorly-formalized and heterogeneous domains as the financial, legal, pharmaceutical and psychological. The system is oriented to provide a customized expert advice, given the pre-designed set of textual templates and the database that contains customers’ profiles and preferences, parameters of products and services, etc. Question-answering is based on matching a formal representation of a query against the formalized representations of answers’ essential ideas (semantic headers of these answers). Semantic headers are designed to be independent on the query phrasing and are the means of approximate reasoning while generating the most relevant advice. A semantic skeleton of an answer includes semantic headers and deductive links between them and their entities, based on the common-sense domain knowledge. Semantic skeleton includes the virtual semantic headers, which do not have to be explicitly programmed but are generated on the fly, using the clauses of semantic skeleton, to be matched with a question.

We present the evaluation of the released question-answering system, advising the customers of H&R Block and CBS Market Watch on various taxes and associated legal issues starting from 1999. Domain development and maintenance implications of semantic header technique, answer accuracy, meaning deviations and overall customer impressions are analyzed. %A Sorin Alexe %A Eugene Blackstone %A Peter L. Hammer %A Hemant Ishwaran %A Michael S. Lauer %A Claire E. Pothier Snader %T Coronary Risk Prediction by Logical Analysis of Data %D March 28, 2002 %Z Tue Apr 23 18:22:34 EDT 2002 %I DIMACS %R 2002-11 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-11.ps.gz %X The objective of this study was to distinguish within a population of patients with known or suspected coronary artery disease groups at high and at low mortality rates. The study was based on Cleveland Clinic Foundation's dataset of 9454 patients, of whom 312 died during an observation period of 9 years. The Logical Analysis of Data method was adapted to handle the disproportioned size of the two groups of patients, and the inseparable character of this dataset -- characteristic to many medical problems. As a result of the study, we have identified a high-risk group of patients representing 1/5 of the population, with a mortality rate 4 times higher than the average, and including 3/4 of the patients who died. The low-risk group identified in the study, representing approximately 4/5 of the population, had a mortality rate 3 times lower than the average. %A Nathaniel Dean %T Mathematical Programming Formulation of Rectilinear Crossing Minimization %D March 28, 2002 %Z Tue Apr 23 18:22:34 EDT 2002 %I DIMACS %R 2002-12 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-12.ps.gz %X In a {\em rectilinear drawing} of a simple graph $G$ each vertex is mapped to a distinct point in the plane and each edge is represented by a straight-line segment with appropriate ends. The goal of rectilinear crossing minimization is to find a rectilinear drawing of $G$ with as few edge crossings as possible. A new approach to rectilinear crossing minimization is presented including a formulation of the problem as a mathematical program with a linear objective function and simple quadratic constraints. Then we size the problem for various graph families. These sizings provide a mechanism for ranking crossing number problems according to their apparent complexity. %A I. E. Zverovich %A I. I. Zverovich %T Graph Ramseian bipartitions and weighted stability %D April 14, 2002 %Z Tue Apr 23 18:22:35 EDT 2002 %I DIMACS %R 2002-13 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-13.ps.gz %X Let P and Q be hereditary classes of graphs. The ordered pair (P, Q) is called {\em Ramseian} if both P and Q are polynomially recognizible, P is \alpha-bounded, and Q is \omega-bounded. Let (P, Q) be an ordered pair of graph classes. We denote by P*Q the class of all graphs G such that there exists a partition A \cup B = V(G) with

where G(X) denotes the subgraph of G induced by a set X \subseteq V(G).
A class of graphs C is called \alpha_w-polynomial if there exists a polynomial-time algorithm for calculation the weighted stability number \alpha_w(G) for all graphs G \in C. A class of graphs C is called \alpha_w-complete if the corresponding decision problem is NP-complete for graphs in C.
Our main result is the following theorem.

Theorem Let (P, Q) be a Ramseian pair.
(i) If Q is an \alpha_w-polynomial class then the class P*Q is also \alpha_w-polynomial.
(ii) If Q is an \alpha_w-complete class then the class P*Q is also \alpha_w-complete.

A similar results for \omega_w-polynomial classes and \omega_w-complete classes are easily follow (\omega_w(G) is the weighted clique number of a graph G). Finally, a recent result of Alekseev and Lozin (2002) is a particular case of our main theorem.

Keywords: Hereditary class, forbidden induced subgraphs, Ramseian partition, weighted stability number. %A Mohamed Haouari %A Mohammad A. Al-Fawzan %T A Bi-objective Model for Maximizing the Quality in Project Scheduling %D April 14, 2002 %Z Tue Apr 23 18:22:36 EDT 2002 %I DIMACS %R 2002-14 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-14.ps.gz %X Traditionally, the Resource Constrained Project Scheduling Problem (RCPSP) is investigated in the operations research literature from the makespan minimization perspective. However, a recent survey conducted in the United States revealed the surprizing fact that the majority of project planners consider maximization of the quality of project schedules as the most important objective (Icmeli Tukel and Rom, 1998). In this paper, the integration of quality in project scheduling is investigated. For that purpose, the problem is modeled as a bi-objective resource-constrained project scheduling problem. A new objective defined as the schedule robustness is introduced as a quality measure. The maximization of this objective is considered along with the makespan minimization. A tabu search algorithm is developped in order to generate an approximate set of efficient solutions. Several variants of the algorithm are tested and compared on a large set of benchmark problems. The results are analyzed using statistical design of experiments techniques.

Keywords : resource-constrained project scheduling, multi-objective combinatorial optimization, tabu search, quality, design of experiments. %A E. Boros %A V. Gurvich %T On Nash-solvability in pure stationary strategies of finite games with perfect information which may have cycles %D April 18, 2002 %Z Tue Apr 23 18:22:37 EDT 2002 %I DIMACS %R 2002-15 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-15.ps.gz %X Let $g$ be a positional game with perfect information modelled by a directed graph $G = (V,E)$ which is finite but may have directed cycles. % an initial position $v_0 \in V(G)$, A local cost function $f(i,e)$ is given for every player $i \in I$ and for every move $e \in E$. The players are allowed only pure stationary strategies, that is the move in any position is deterministic, and may depend only on this present position, not on the preceding positions or moves. Hence, the resulting play $p$ is a directed path which begins in the initial position $v_0$ and either (i) ends in a final position or (ii) results in a simple directed cycle. Given a play $p$, for every player $i \in I$ the effective cost $f(i,p)$ is defined as the sum of all local costs along the path $f(i,p) = \sum_{e \in p} f(i,e)$ in case of (i), or as $f(i,p) = + \infty$ in case of (ii). Let us call a local cost function $f$ and the corresponding game terminal if $f(i,e) = 0$ for every player $i \in I$ and for every move $e$ which is not leading to a final position. The players wish to minimize their effective costs, thus in particular they should try to avoid cycles. A game is called Nash-solvable if it has at least one Nash equilibrium in pure stationary strategies and properly Nash-solvable if the corresponding play results in a final position, not in a cycle. It is easy to demonstrate that already zero-sum games with two players may not be solvable. Yet, Nash-solvability turns into an exciting open problem under the following simple additional condition: ($\clubsuit$) all local costs are non-negative, i.e. $f(i,e) \geq 0$ for every player $i \in I$ for every move $e \in E$, or under the seemingly weaker but in fact equivalent condition: ($\spadesuit$) $\sum_{e \in c} f(i,e) \geq 0$, for every player $i \in I$ and for every simple directed cycle $c$ in $G$.
In all examples, which we were able to analyze, games satisfying condition ($\clubsuit$) turned out to be properly Nash-solvable, yet the Nash-solvability of such games is an open problem. In this paper we prove proper Nash-solvability for the following special cases: (a) play-once games, i.e. games in which every player controls exactly one position, (b) terminal games with only 2 players, and (c) terminal games with only 2 terminal moves. We also show that in each of these cases a Nash equilibrium can be constructed in polynomial time in the size of the graph $G$.

Keywords: cycle, cyclic game, directed graph, directed cycle, directed path, effective cost, local cost, Nash equilibrium, perfect information, positional game, potentials, pure strategies, saddle point, stationary strategies, strong equilibrium, shortest path. %A Viacheslav Prelov %A Sergio Verd\'u %T Second-order Asymptotics of Mutual Information %D April 19, 2002 %Z Tue Apr 23 18:22:38 EDT 2002 %I DIMACS %R 2002-16 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-16.ps.gz %X A formula for the second-order expansion of the input-output mutual information of multidimensional channels as the signal-to-noise ratio goes to zero is obtained. While the additive noise is assumed to be Gaussian, we deal with very general classes of input and channel distributions. As special cases, these channel models include fading channels, channels with random parameters and channels with almost Gaussian noise. When the channel is unknown at the receiver, the second term in the asymptotic expansion depends not only on the covariance matrix of the input signal but also on the fourth mixed moments of its components. The second-order asymptotics of mutual information finds application in the analysis of the bandwidth-power tradeoff achieved by specific (not necessarily optimum) input signaling in the wideband regime.

Keywords: Mutual Information, Channel Capacity, Fading Channels, Nonlinear Channels, Low-power communication. %A Alberto Roverato %A Guido Consonni %T Compatible Prior Distributions for DAG models %D April 19, 2002 %Z Tue Apr 23 18:22:39 EDT 2002 %I DIMACS %R 2002-17 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-17.ps.gz %X The application of certain Bayesian techniques, such as the Bayes Factor and model averaging, requires the specification of prior distributions on the parameters of alternative models. We propose a new method for constructing compatible priors on the parameters of models nested in a given DAG (Directed Acyclic Graph) model, using a conditioning approach. We define a class of parameterisations consistent with the modular structure of the DAG and derive a procedure, invariant within this class, which we name reference conditioning.

Keywords: Bayes factor; Directed acyclic graph; Fisher information matrix; Graphical model; Invariance; Jeffreys conditioning; Group reference prior; Reference conditioning; Reparameterisation. %A Boris Galitsky %A Andrey Dementiev %A Sergey Shelepin %T The set of pair-wise correlated sequence positions contributes to determination of the immunoglobulin fold %D April 23, 2002 %Z Tue Apr 23 18:22:40 EDT 2002 %I DIMACS %R 2002-18 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-18.ps.gz %X In this study, we are resolving the contradiction that rather limited number of residues or classes of amino acids (about 10) determines the fold (Immunoglobulin-like) for the sequence of about 100 residues long. Immunoglobulin fold comprises the protein super-families with rather distinguishing sequences with less than 10% identity; their sequence alignment can be accomplished only taking into account the 3D structure. Therefore, we believe that discovering the additional common features of the sequences is necessary to explain the existence of common fold for these (SCOP) superfamilies. The analysis of pair-wise interconnection between residues of the multiple sequence alignment helped us to reveal the set of mutually correlated positions, inherent to almost every super-family of protein fold. Hence, the set of constant positions plus the set of variable but mutually correlated ones can serve as a basis of having the common 3D structure for rather distinguishing protein sequences. %A Vasek Chvatal %T Sylvester-Gallai theorem and metric betweenness %D April 26, 2002 %Z Fri Jul 12 15:43:03 EDT 2002 %I DIMACS %R 2002-19 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-19.ps.gz %X Sylvester conjectured in 1893 and Gallai proved some forty years later that every finite set S of points in the plane includes two points such that the line passing through them includes either no other point of S or all other points of S. There are several ways of extending the notion of lines from Euclidean spaces to arbitrary metric spaces. We present one of them and conjecture that, with lines in metric spaces defined in this way, the Sylvester-Gallai theorem generalizes as follows: in every finite metric space, there is a line consisting of either two points or all the points of the space. Then we present slight evidence in support of this rash conjecture and finally we discuss the underlying ternary relation of metric betweenness. %A Matthew Andrews %A Antonio Fern\'andez %A Ashish Goel %A Lisa Zhang %T Source Routing and Scheduling in Packet Networks %D Apr 26, 2002 %Z Fri Jul 12 15:44:42 EDT 2002 %I DIMACS %R 2002-20 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-20.ps.gz %X

We study {\em routing} and {\em scheduling} in packet-switched networks. We assume an adversary that controls the injection time, source, and destination for each packet injected. A set of paths for these packets is {\em admissible} if no link in the network is overloaded. We present the first on-line routing algorithm that finds a set of admissible paths whenever this is feasible. Our algorithm calculates a path for each packet as soon as it is injected at its source using a simple shortest path computation. The length of a link reflects its current congestion. We also show how our algorithm can be implemented under today's Internet routing paradigms.

When the paths are known (either given by the adversary or computed as above) our goal is to schedule the packets along the given paths so that the packets experience small end-to-end delays. The best previous delay bounds for deterministic and distributed scheduling protocols were exponential in the path length. In this paper we present the first deterministic and distributed scheduling protocol that guarantees a polynomial end-to-end delay for every packet.

Finally, we discuss the effects of combining routing with scheduling. We first show that some unstable scheduling protocols remain unstable no matter how the paths are chosen. However, the freedom to choose paths can make a difference. For example, we show that a ring with parallel links is stable for all greedy scheduling protocols if paths are chosen intelligently, whereas this is not the case if the adversary specifies the paths. %A Mayur Datar %A S. Muthukrishnan %T Estimating Rarity and Similarity over Data Stream Windows %D Apr 30, 2002 %Z Fri Jul 12 15:51:09 EDT 2002 %I DIMACS %R 2002-21 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-21.ps.gz %X In the windowed data stream model, we observe items coming in over time. At any time $t$, we consider the window of the last $N$ observations $a_{t-(N-1)},a_{t-(N-2)},\ldots,a_t$, each $a_i \in \{1,\ldots,u\}$; we are allowed to ask queries about the data in the window, say, we wish to compute the minimum or the median of the items in the window. A crucial restriction is that we are only allowed $o(N)$ (often polylogarithmic in $N$) storage space, that is, space smaller than the window size, so the items within the window can not be archived. Window data stream model arose out of the need to formally reason about the underlying data analyses problems in applications like inter-networking and transactions processing.

In this paper, we study two basic problems in the windowed data stream model. The first is the estimation of the rarity of items in the window. While previous work has studied simple distributional parameters such as the number of distinct items in the window, no prior work has addressed the general problem of estimating the rarity. Our second problem is one of estimating similarity between two data stream windows using the Jacard's coefficient. Prior work has focused on $L_p$ norms and set similarity measures such as the Jacard's coefficient have been studied before in the windowed data stream model. The problems of estimating rarity and similarity have many applications in mining massive data.

We present novel, simple algorithms for estimating rarity and similarity on windowed data streams, accurate up to factor $1 \pm \epsilon$ using space only logarithmic in the window size. In both cases, our solutions are based on modifications of the powerful min-wise hashing technique. We expect our solutions to find applications in practice. %A Rosario Gennaro %A Yael Gertner %A Jonathan Katz %T Bounds on the Efficiency of Encryption and Digital Signatures %D May 7, 2002 %Z Fri Jul 12 15:51:37 EDT 2002 %I DIMACS %R 2002-22 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-22.ps.gz %X A central focus of modern cryptography is to investigate the weakest possible assumptions under which various cryptographic algorithms exist. Typically, a proof that a ``weak'' primitive (e.g., a one-way function) implies the existence of some ``strong'' algorithm (e.g., a private-key encryption scheme) proceeds by giving an explicit construction of the latter from the former. Beyond merely showing such a construction, an equally important research direction is to explore the efficiency of the construction. One might argue that this line of research has become even more important now that minimal assumptions are known for many (but not all) algorithms of interest.

Protocols for encryption (in both the public- and private-key setting) and for digital signatures are fundamental to cryptography. In this work, we show the first lower bounds on the efficiency of constructions of these protocols based on black-box access to one-way or trapdoor one-way permutations. If $S$ is the assumed security of the permutation $\pi$ (i.e., no adversary of size $S$ can ``break'' $\pi$ in the appropriate sense on a fraction larger than $1/S$ of its inputs), our results show that:

We prove our results in an extension of the Impagliazzo-Rudich model. That is, we show that any black-box construction beating our lower bounds would imply the unconditional existence of a one-way function. %A Endre Boros %A Khaled Elbassioni %A Vladimir Gurvich %A Leonid Khachiyan %T Generating Dual-Bounded Hypergraphs %D May 10, 2002 %Z Fri Jul 12 15:51:49 EDT 2002 %I DIMACS %R 2002-23 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-23.ps.gz %X

This paper surveys some recent results on the generation of implicitly given hypergraphs and their applications in Boolean and integer programming, data mining, reliability theory, and combinatorics.

Given a monotone property $\pi$ over the subsets of a finite set $V$, we consider the problem of incrementally generating the family $\cF_{\pi}$ of all minimal subsets satisfying property $\pi$, when $\pi$ is given by a polynomial-time satisfiability oracle. For a number of interesting monotone properties, the family $\cF_{\pi}$ turns out to be {\em uniformly dual-bounded}, allowing for the incrementally efficient enumeration of the members of $\cF_{\pi}$.

Important applications include the efficient generation of minimal infrequent sets of a database (data mining), minimal connectivity ensuring collections of subgraphs from a given list (reliability theory), minimal feasible solutions to a system of monotone inequalities in integer variables (integer programming), minimal spanning collections of subspaces from a given list (linear algebra) and maximal independent sets in the intersection of matroids (combinatorial optimization).

In contrast to these results, the analogous problem of generating the family of all maximal subsets not having property $\pi$ is NP-hard for most of the monotone properties $\pi$ considered in the paper. %A Brenda J. Latka %T A Classification of Antichains of Finite Tournaments %D May 10, 2002 %Z Fri Jul 12 15:52:02 EDT 2002 %I DIMACS %R 2002-24 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-24.ps.gz %X Tournament embedding is an order relation on the class of finite tournaments. An antichain is a set of finite tournaments that are pairwise incomparable in this ordering. We say an antichain ${\cal A}$ can be extended to an antichain ${\cal B}$ if ${\cal A}\subseteq {\cal B}$. Those finite antichains that can not be extended to antichains of arbitrarily large finite cardinality are exactly those that contain a member of each of four families of tournaments. We give an upper bound on the cardinality of extensions of such antichains. This bound depends on the maximum order of the tournaments in the antichain. %A Yevgeniy Dodis %A Jonathan Katz %A Shouhuai Xu %A Moti Yung %T Strong Key-Insulated Signature Schemes %D May 30, 2002 %Z Fri Jul 12 15:52:16 EDT 2002 %I DIMACS %R 2002-25 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-25.ps.gz %X

Signature computation is frequently performed on insecure devices --- e.g., mobile phones --- operating in an environment where the private (signing) key is likely to be exposed. Strong key-insulated signature schemes are one way to mitigate the damage done when this occurs. In the key-insulated model \cite{DKXY02}, the secret key stored on an insecure device is refreshed at discrete time periods via interaction with a physically-secure device which stores a ``master key''. All signing is still done by the insecure device, and the public key remains fixed throughout the lifetime of the protocol. In a strong $(t, N)$-key-insulated scheme, an adversary who compromises the insecure device and obtains secret keys for up to $t$ periods is unable to forge signatures for any of the remaining $N-t$ periods. Furthermore, the physically-secure device (or an adversary who compromises only this device) is unable to forge signatures for \emph{any} time period.

We present here constructions of strong key-insulated signature schemes based on a variety of assumptions. First, we demonstrate %and prove secure a generic construction of a strong $(N-1, N)$-key-insulated signature scheme using any standard signature scheme. We then give a %an improved construction of a strong $(t, N)$-signature scheme whose security may be based on the discrete logarithm assumption in the random oracle model. This construction offers faster signing and verification than the generic construction, at the expense of $O(t)$ key update time and key length. % We then give an improved construction of a strong $(t, N)$-signature %scheme whose security may be based on the discrete logarithm %assumption in the random oracle model. Finally, we construct strong $(N-1,N)$-key-insulated schemes based on any ``trapdoor signature scheme'' (a notion we introduce here); our resulting construction in fact serves as an identity-based signature scheme as well. This leads to very efficient solutions based on, e.g., the RSA assumption in the random oracle model. %A Khaled M. Elbassioni %T An Algorithm for Dualization in Products of Lattices %D May 30, 2002 %Z Fri Jul 12 15:52:33 EDT 2002 %I DIMACS %R 2002-26 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-26.ps.gz %X Let $\cL=\cL_1\times\cdots\times\cL_n$ be the product of $n$ lattices, each of which has a bounded width. Given a subset $\cA\subseteq\cL$, we show that the problem of extending a given partial list of maximal independent elements of $\cA$ in $\cL$ can be solved in quasi-polynomial time. %A Endre Boros %A Khaled Elbassioni %A Vladimir Gurvich %A Leonid Khachiyan %T Extending the Balas-Yu Bounds on the Number of Maximal Independent Sets in Graphs to Hypergraphs and Lattices %D Jun 3, 2002 %Z Fri Jul 12 15:52:45 EDT 2002 %I DIMACS %R 2002-27 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-27.ps.gz %X A result of Balas and Yu (1989) states that the number of maximal independent sets of a graph $G$ is at most $\delta^{p} + 1$, where $\delta$ is the number of pairs of vertices in $G$ at distance 2, and $p$ is the cardinality of a maximum induced matching in $G$. In this paper, we give an analogue of this result for hypergraphs and, more generally, for subsets of vectors $\cB$ in the product of $n$ lattices $\cL=\cL_1\times\cdots\times\cL_n$, where the notion of an induced matching in $G$ is replaced by a certain binary tree each internal node of which is mapped into $\cB$. We show that our bounds may be nearly sharp for arbitrarily large hypergraphs and lattices. As an application, we prove that the number of maximal infeasible vectors $x \in \cL=\cL_1\times\cdots\times\cL_n$ for a system of polymatroid inequalities $f_1(x) \ge t_1,\ldots,f_r(x) \ge t_r$ does not exceed $\max\{Q,\beta^{\log t/c(2Q,\beta)}\}$, where $\beta$ is the number of minimal feasible vectors for the system, $Q=|\cL_1|+\ldots+|\cL_n|$, $t=\max\{t_1,\ldots,t_r\}$, and $c(\rho,\beta)$ is the unique positive root of the equation $2^c(\rho^{c/\log \beta}-1)=1$. This bound is nearly sharp for the Boolean case $\cL=\{0,1\}^n$, and it allows for the efficient generation of all minimal feasible sets to a given system of polymatroid inequalities with quasi-polynomially bounded right-hand sides $t_1, \ldots, t_m$. %A I. E. Zverovich %T The Domination Number of $(K_p, P_5)$-Free Graphs %D Jun 7, 2002 %Z Fri Jul 12 15:52:56 EDT 2002 %I DIMACS %R 2002-28 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-28.ps.gz %X We prove that, for each $p \ge 1$, there exists a polynomial time algorithm for finding a minimum domination set in the class of all $(K_p, P_5)$-free graphs. %A L. Becchetti %A S. Diggavi %A S. Leonardi %A A. Marchetti-Spaccamela %A S. Muthukrishnan %A T. Nandagopal %A A. Vitaletti %T Parallel Scheduling Problems in Next Generation Wireless Networks %D Jun 7, 2002 %Z Fri Jul 12 15:55:31 EDT 2002 %I DIMACS %R 2002-29 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-29.ps.gz %X Next generation 3G/4G wireless data networks allow multiple codes (or channels) to be allocated to a single user, where each code can support multiple data rates. Providing fine-grained QoS to users in such networks poses the two dimensional challenge of assigning {\em both} power (rate) and codes for every user. This gives rise to a new class of parallel scheduling problems. We abstract general downlink scheduling problems suitable for proposed next generation wireless data systems. This includes a communication-theoretic model for multirate wireless channels. In addition, while conventional focus has been on throughput maximization, we attempt to optimize the maximum response time of jobs, which is more suitable for stream of user requests. We present provable results on the algorithmic complexity of these scheduling problems. In particular, we are able to provide very simple, online algorithms for approximating the optimal maximum response time. This relies on resource augmented competitive analysis. We also perform an experimental study with realistic data of channel conditions and user requests to show that our algorithms are more accurate than our worst case analysis shows, and they provide fine-grained QoS to users effectively. %A Yan Wang %A Xin Gui Fang %A D. Frank Hsu %T On the Edge-Forwarding Indices of Frobenius Graphs %D Jun 19, 2002 %Z Fri Jul 12 15:55:32 EDT 2002 %I DIMACS %R 2002-30 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-30.ps.gz %X A $G$-Frobenius graph, as defined recently by Fang, Li, and Praeger, is a connected orbital graph of a Frobenius group $G=K{:}H$ with Frobenius kernel $K$ and Frobenius complement $H$. $\Gamma$ is also shown to be a Cayley graph, $\Gamma=Cay(K,S)$ for $K$ and some subset $S$ of the group $G$. On the other hand, a network $N$ with a routing function $R$, written as $(N,R)$, is an undirected graph $N$ together with a routing $R$ which consists of a collection of simple paths connecting every pair of vertices in the graph. The edge-forwarding index $\pi(\Gamma)$ of a network $(N,R)$, defined by Heydemann, Meyer, and Sotteau, is a parameter to describe the maximum load of edges of $N$. In this paper, we study the edge-forwarding index of Frobenius graphs. In particular, we obtain edge-forwarding index of a $G$-Frobenius graph $\Gamma$ with rank$(G)\leq 50$ and those of $\Gamma$ which has $type-(n_1,n_2,...,n_d)$ where $d=n,(1,2,3,...,n); d=2n-1,(1,2,...,n-1,n,n-1,...,2,1); d=2n,(1,2,...,n-1,n,n,n-1,...2,1)$, respectively. %A Brenda J. Latka %T The Well-quasi-ordered Class of Tournaments Defined by the Forbidden Subtournament $N_5$ %D Jul 21, 2002 %Z Fri Oct 11 18:50:13 EDT 2002 %I DIMACS %R 2002-31 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-31.ps.gz %X The tournament $N_5$ can be obtained from the transitive tournament on $\{1,\ldots,5\}$, with the natural order, by reversing the edges between successive vertices. Tournaments that do {\em not} have $N_5$ as a subtournament are said to {\em omit} $N_5$. We describe the structure of tournaments that omit $N_5$ and use this with Kruskal's Tree Theorem to prove that this class of tournaments is well-quasi-ordered. The proof involves an encoding of the indecomposable tournaments omitting $N_5$ by a finite alphabet.

The main technical problem is giving an explicit description of the indecomposable tournaments omitting $N_5$. The key to the proof that the explicit description is complete is the observation that for any indecomposable tournament $T$ with $n>1$ vertices, there is a proper indecomposable subtournament of $T$ with $n-2$ or $n-1$ vertices. Thus the claim can be verified by a natural inductive procedure; it suffices to check that for any tournament $T$ in the explicitly given list, any indecomposable extension of $T$ by at most 2 vertices that omits $N_5$ will also be found in our list. %A Alexander Barg %A Gilles Zémor %T Error exponents of expander codes under linear-complexity decoding %D Jul 21, 2002 %Z Fri Oct 11 18:50:14 EDT 2002 %I DIMACS %R 2002-32 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-32.ps.gz %X

A class of codes is said to reach capacity $\cC$ of the binary symmetric channel if for any rate $R<\cC$ and any $\varepsilon>0$ there is a sufficiently large $N$ such that codes of length $\ge N$ and rate $R$ from this class provide error probability of decoding at most $\varepsilon$, under some decoding algorithm.

The study of the error probability of expander codes was initiated in Barg and Z{\'e}mor (2002), where it was shown that they attain capacity of the binary symmetric channel under a linear-time iterative decoding with error probability falling exponentially with code length $N$. In this work we study variations on the expander code construction and focus on the most important region of code rates, close to the channel capacity. For this region we estimate the decrease rate (the error exponent) of error probability of decoding for randomized ensembles codes. The resulting estimate gives a substantial improvement of previous results for expander codes and some other explicit code families. %A R. Collado %A A. Kelmans %A D. Krasner %T On Convex Polytopes in the Plane "Containing" and "Avoiding" Zero %D Jul 26, 2002 %Z Fri Oct 11 18:50:14 EDT 2002 %I DIMACS %R 2002-33 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-33.ps.gz %X

Let be a finite set of points in the plane, X be a subset of S, and z be a point not in S. X is a z-containing set if z is in the interior of the convex hull of X. Also X is a z-avoiding set if z is not contained in the interior of the convex hull of X. Let C(S) and A(S) denote the sets of minimal z-containing and maximal z-avoiding subsets of S.

E. Boros and V. Gurvich raised the following question:

Is it true that |A(S)| is less than or equal to 2d |C(S)| where d is the dimension of the space?

This inequality is obviously true for d = 1.

In this paper we verify the inequality for d = 2 by proving the following stronger result:

Theorem: Let S be a finite set of points in the plane and z a point not in S. Suppose that z is in the interior of the convex hull of S. Then |A(S)| less than or equal to 3 |C(S)| + 1. Moreover, the equality holds if and only if |S| = 4, the convex hull of S is a quadrilateral Q, and z is the point of intersection of the two diagonals of Q. %A Endre Boros %A Vladimir Gurvich %A Steven Jaslar %A Daniel Krasner %T Stable Matchings in Three-Sided Systems with Cyclic Preferences %D Aug 16, 2002 %Z Fri Oct 11 18:50:15 EDT 2002 %I DIMACS %R 2002-34 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-34.ps.gz %X We consider generalizations of the Gale-Shapley (1962) Stable Marriage Problem to three-sided families. Alkan (1988) gave an example which shows that in this case stable matchings do not always exist. Here we provide a simpler example demonstrating this fact. Danilov (2001) proved that stable matchings always exist for the special case of certain acyclic preferences and he raised the problem for another special case involving cyclic preferences. Here we show that the answer is still negative by constructing a three-sided system with lexicographically cyclic preferences for which no stable matching exists. Finally, we also consider possible generalizations to $m$-sided families, for $m>3$.

Keywords: Gale-Shapley Theorem, stable matching, stable marriage, cyclic preferences. %A Graham Cormode %A S. Muthukrishnan %T Estimating Dominance Norms of Multiple Data Streams %D Aug 16, 2002 %Z Fri Oct 11 18:50:15 EDT 2002 %I DIMACS %R 2002-35 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-35.ps.gz %X Data streams often consist of multiple signals. Consider a stream of multiple signals (i,a_i,j) where i's correspond to the domain, j's index the different signals and a_i,j >= 0 to the value of the j'th signal at point i. We study the problem of determining the dominance norms over the multiple signals, in particular the max-dominance norm, defined as sum_i max_j {a_i,j}. It is used in applications to estimate the ``worst case influence'' of multiple processes, for example in IP traffic analysis, electrical grid monitoring and financial domain. Besides finding many applications, it is a natural measure: it generalizes the notion of union of data streams and may be alternately thought of as estimating the L1 norm of the upper envelope of multiple signals.

We present the first known data stream algorithm for estimating max-dominance of multiple signals. In particular, we use workspace and time-per-item that are both sublinear (in fact, poly-logarithmic) in the input size. The algorithm is simple and implementable; its analysis relies on using properties of stable random distributions with small parameter alpha, which may be a technique of independent interest. In contrast we show that other dominance norms -- min-dominance sum_i min_j {a_i,j}, count-dominance (|{i | a_i > b_i}|) or relative-dominance (sum_i a_i/max{1,b_i}), are all impossible to estimate accurately with sublinear space. %A Alexander Barg %A Gregory Kabatiansky %T A class of i.p.p. codes with efficient identification %D Aug 30, 2002 %Z Fri Oct 11 18:50:18 EDT 2002 %I DIMACS %R 2002-36 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-36.ps.gz %X Let C be a code of length n over a q-ary alphabet. An n-word y is called a descendant of a set of t codewords x^1,...,x^t if y_i \in {x^1_i,...,x^t_i} for all i=1,...,n. A code is said to have the t-identifying parent property (t-i.p.p.) if for any n-word y that is a descendant of at most t parents it is possible to identify at least one of them.

An explicit construction is presented of t-i.p.p. codes of rate bounded away from zero, for which identification can be accomplished with complexity poly(n). %A Paul Lemke %A Steven S. Skiena %A Warren D. Smith %T Reconstructing Sets From Interpoint Distances %D Sep 5, 2002 %Z Fri Oct 11 18:50:19 EDT 2002 %I DIMACS %R 2002-37 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-37.ps.gz %X Which point sets realize a given distance multiset? Interesting cases include the ``turnpike problem'' where the points lie on a line, the ``beltway problem'' where the points lie on a loop, and multidimensional versions. We are interested both in the algorithmic problem of determining such point sets for a given collection of distances and the combinatorial problem of finding bounds on the maximum number of different solutions. These problems have applications in genetics and crystallography.

We give an extensive survey and bibliography in an effort to connect the independent efforts of previous researchers, and present many new results. In particular, we give improved combinatorial bounds for the turnpike and beltway problems. We present a pseudo-polynomial time algorithm as well as a practical $\bigo ( 2^n n \log n )$-time algorithm that find all solutions to the turnpike problem, and show that certain other variants of the problem are NP-hard. We conclude with a list of open problems. %A V.E. Alekseev %A D.V. Korobitsyn %A V.V. Lozin %T Boundary classes of graphs for the dominating set problem %D Sep 12, 2002 %Z Fri Oct 11 18:50:20 EDT 2002 %I DIMACS %R 2002-38 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-38.ps.gz %X The notion of a boundary class has been recently introduced as a tool for classification of hereditary classes of graphs according to the time complexity of NP-hard graph problems. In the present paper we concentrate on the dominating set problem and obtain three boundary classes for it. %A Carlos Castillo-Chavez %A Fred S. Roberts %T Report on DIMACS Working Group Meeting: Mathematical Sciences Methods for the Study of Deliberate Releases of Biological Agents and their Consequences %D Sep 18, 2002 %Z Fri Oct 11 18:50:21 EDT 2002 %I DIMACS %R 2002-39 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-39.ps.gz %X Report on DIMACS Working Group Meeting: Mathematical Sciences Methods for the Study of Deliberate Releases of Biological Agents and their Consequences %A Fred S. Roberts %T Challenges for Discrete Mathematics and Theoretical Computer Science in the Defense Against Bioterrorism %D Sep 22, 2002 %Z Fri Oct 11 18:50:21 EDT 2002 %I DIMACS %R 2002-40 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-40.ps.gz %X Dealing with bioterrorism requires detailed planning of preventive measures and responses. Both planning and response require precise reasoning and extensive analysis of the type that mathematical scientists are very good at. Discrete mathematics and theoretical computer science, broadly defined, seem very relevant. We describe challenges for discrete mathematics and theoretical computer science raised by the need to plan for and defend against bioterrorist attacks %A Victoria Ungureanu %A Phillip G. Bradford %A Michael Katehakis %A Benjamin Melamed. %T Deferred Assignment Scheduling in Clustered Web Servers %D Oct 1, 2002 %Z Fri Oct 11 18:50:23 EDT 2002 %I DIMACS %R 2002-41 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-41.ps.gz %X This paper proposes new scheduling policies for clustered servers, which are based on job size. The proposed algorithms are shown to be efficient, simple and easy to implement. They differ from traditional methods in the way jobs are assigned to back-end servers. The main idea is to defer scheduling as much as possible in order to make better use of the accumulated information on job sizes. Furthermore, the proposed algorithms are designed to work effectively with the class of job-size distributions often encountered on the Internet. To gauge the efficacy of the proposed algorithms, the paper presents an empirical case study that shows these algorithms perform well on input from real-life trace data measured at Internet clustered servers. %A Boris Galitsky %A Dmitry Vinogradov %T Using reasoning about dynamic domains and inductive reasoning for automatic processing of claims %D Oct 17, 2002 %Z Fri Dec 13 10:55:03 EDT 2002 %I DIMACS %R 2002-42 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-42.ps.gz %X We report on the novel approach to modeling a dynamic domain with limited knowledge. Such domain may include participating agents such that we are uncertain about motivations and decision-making principles of some of these agents. Our model for such domain includes the deductive and inductive components. The former component is based on situation calculus and describes the behavior of agents with complete information. The latter machine learning-based inductive component that involves its previous experience in prediction the agents^Ò actions.

Suggested reasoning machinery is applied to the problem of processing of claims of unsatisfied customers. The task is to predict the future action of a participating agent (the company that has upset the customer) to determine the required course of actions to settle down the claim. We believe our framework reflect the general setting of reasoning in a dynamic domains in the conditions of uncertainty, merging analytical and analogy-based reasoning. %A I. E. Zverovich %T Unique domination and domination perfect graphs %D Oct 17, 2002 %Z Fri Dec 13 10:55:04 EDT 2002 %I DIMACS %R 2002-43 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-43.ps.gz %X We review a characterization of domination perfect graphs in terms of forbidden induced subgraphs obtained by Zverovich and Zverovich \cite{ZverovichZ95} using a computer code. Then we apply it to a problem of unique domination in graphs recently proposed by Fischermann and Volkmann. %A Andreas Brandstadt %A Peter L. Hammer %A Van Bang Le %A Vadim V. Lozin %T Bisplit Graphs %D Oct 24, 2002 %Z Fri Dec 13 10:55:05 EDT 2002 %I DIMACS %R 2002-44 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-44.ps.gz %X A graph is bisplit if it can be partitioned into a stable set and a bi-clique (i.e. a complete bipartite graph). We provide an O(nm) recognition algorithm for these graphs, and characterize them in terms of forbidden induced subgraphs. Moreover, we show that the recognition problem of the slightly larger class of weak bisplit graphs is NP-complete. %A Vadim Mottl %A Ilya Muchnik %T Serial and tree-serial dynamic programming with application to fact identification %D Nov 15, 2002 %Z Fri Dec 13 10:55:06 EDT 2002 %I DIMACS %R 2002-45 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-45.ps.gz %X This report continues the series of DIMACS Technical Reports on the variational approach to constructing algorithms of data analysis that consists in systematically exploiting the fact that all the kinds of decision making rest on the intent, at least, a mental one, to minimize an appropriate measure of discrepancy between the observed data set and result of its processing in the form of a model of the original data set to be evaluated. The specificity of the optimization problems adequate to a majority of practical data analysis problems is that the variables constituting the sought-for data set model are associated with the nodes of a graph that determines its a priori structure. As a rule, the objective function to be minimized turns out to be pair-wise separable in accordance with this graph, i.e. be the sum of partial functions of one and two variables associated with nodes and edges of graph.

However, for a separable objective function of general kind, the problem of global optimization does not lend itself to an effective algorithmical solution until the variable adjacency graph is assumed to be a tree. For this latter kind of objective functions, the original optimization problem breaks up into a hierarchy of partial problems each of which consists in the optimization of a set of functions of only one variable. The proposed principle of solving tree-like pair-wise separable optimization problems on the basis of a hierarchical elimination of variables is called in this Report the tree-serial dynamic programming as a generalization of the classical serial dynamic programming.

Such a structure of the interaction of variables in an objective function is an intermediate special case between easily solvable serial problems and challenging nonserial ones. It is shown, that such a moderate generalization, on the one hand, retains practically all the computational advantages of the serial problems and, on the other, easily allows for using it, with a bit of heuristics, in solving typical image processing problems.

As a practical problem, we address in this work the problem of face recognition from a single image. The tree-serial dynamic programming is applied to fulfill a nonlinear transformation of one image plane relative to another by spatially constrained elastic matching of two pixel grids for the purpose of featureless face identification by immediate measuring image similarity. The method provides the linear computational complexity with respect to the number of pixels without application of parallel computers.

It will be shown in the next Report that the proposed approach is adequate, along with the problem of face identification, also the problems of face detection and tracking in an image flow and, so, covers the entire concept of dynamic vision. %A Philip MacKenzie %T The PAK Suite: Protocols for Password-Authenticated Key Exchange %D Oct 24, 2002 %Z Fri Dec 13 10:55:07 EDT 2002 %I DIMACS %R 2002-46 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-46.ps.gz %X In this paper we give a detailed formal description of the PAK password-authenticated key exchange protocol and some variants, and provide provide complete proofs of security which we believe are more straightforward than the original proofs. We also show a new general method (called the Z-method) for making these protocols resilient to server-compromise, so as to not allow an attacker that obtains password verification data from a server to then impersonate a user. When this method is applied to PAK, we call the resulting protocol PAK-Z. Finally, we discuss the current state-of-the-art in password-authenticated key exchange, with respect to both theory and practice. %A I. E. Zverovich %A I. I. Zverovich %T Ratio of generalized parameters %D Nov 12, 2002 %Z Fri Dec 13 10:55:08 EDT 2002 %I DIMACS %R 2002-47 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-47.ps.gz %X

Let ${\mathcal{P}}$ be a class of graphs. A {\em ${\mathcal{P}}$-set} in a graph $G$ is a vertex subset $X$ such that $G(X) \in {\mathcal{P}}$. We define the {\em ${\mathcal{P}}$-stability number} of a graph $G$, $\alpha_{\mathcal{P}}(G)$, as the maximum cardinality of a ${\mathcal{P}}$-set in $G$.

A {\em ${\mathcal{P}}$-dominating set} in a graph is a dominating ${\mathcal{P}}$-set. Accordingly, the {\em ${\mathcal{P}}$-domination number} of a graph $G$, $\gamma_{\mathcal{P}}(G)$, is the minimum cardinality of a ${\mathcal{P}}$-dominating set in $G$.

For each $r \ge 1$, we define a graph $G$ to be an {\em $\alpha_{\mathcal{P}}/\gamma_{\mathcal{Q}}(r)$-perfect graph} if $\alpha_{\mathcal{P}}(H)/\gamma_{\mathcal{Q}}(H) \le r$ for each induced subgraph $H$ of $G$.

We characterize all classes of $\alpha_{\mathcal{P}}/\gamma_{\mathcal{Q}}(r)$-perfect graphs in terms of forbidden induced subgraphs for all hereditary classes ${\mathcal{P}}$ and ${\mathcal{Q}}$ containing all edgeless graphs, and for all real numbers $r \ge 1$. We propose a number of related open problems and conjectures. %A N. V. R. Mahadev %A Fred S. Roberts %T Consensus List Colorings of Graphs and Physical Mapping of DNA %D Nov 13, 2002 %Z Fri Dec 13 10:55:09 EDT 2002 %I DIMACS %R 2002-48 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-48.ps.gz %X In graph coloring, one assigns a color to each vertex of a graph so that neighboring vertices get different colors. We shall talk about a bioconsensus problem relating to graph coloring and discuss the applicability of the ideas to the DNA physical mapping problem. In many applications of graph coloring, one gathers data about the acceptable colors at each vertex. A list coloring is a graph coloring so that the color assigned to each vertex belongs to the list of acceptable colors associated with that vertex. We consider the situation where a list coloring cannot be found. If the data contained in the lists associated with each vertex are made available to individuals associated with the vertices, it is possible that the individuals can modify their lists through trades or exchanges until the group of individuals reaches a set of lists for which a list coloring exists. We describe several models under which such a consensus set of lists might be attained. In the physical mapping application, the lists consist of the sets of possible copies of a target DNA molecule from which a given clone was obtained and trades or exchanges correspond to correcting errors in data. %A Gabriela Alexe %A Sorin Alexe %A Peter L. Hammer %A Alexander Kogan %T Comprehensive vs. Comprehensible Classifiers in Logical Analysis of Data %D Dec 4, 2002 %Z Fri Dec 13 10:55:11 EDT 2002 %I DIMACS %R 2002-49 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-49.ps.gz %X The main objective of this paper is to compare the classification accuracy provided large, comprehensive collections of patterns (rules) derived from archives of past observations, with that provided by small, comprehensible collections of patterns. This comparison is carried out here on the basis of an empirical study, using several publicly available datasets. The results of this study show that the use of comprehensive collections allows a slight increase of classification accuracy, and that the cost of comprehensibility is small. %A Gabriela Alexe %A Peter L. Hammer %T Spanned Patterns for the Logical Analysis of Data %D Dec 4, 2002 %Z Fri Dec 13 10:55:11 EDT 2002 %I DIMACS %R 2002-50 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-50.ps.gz %X In a finite dataset consisting of positive and negative observations represented as real valued n-vectors, a positive (negative) pattern is an interval in Rn with the property that it contains sufficiently many positive (negative) observations, and sufficiently few negative (positive) ones. A pattern is spanned if it does not include properly any other interval containing the same set of observations. Although large collections of spanned patterns can provide highly accurate classification models within the framework of the Logical Analysis of Data, no efficient method for their generation is currently known. We propose in this paper an incrementally polynomial time algorithm for the generation of all spanned patterns in a dataset, which runs in linear time in the output; the algorithm resembles closely the Blake and Quine consensus method for finding the prime implicants of Boolean functions. The efficiency of the proposed algorithm is tested on various publicly available datasets. In the last part of the paper, we present the results of a series of computational experiments which show the high degree of robustness of spanned patterns. %A Sorin Bastea %A Raffaele Esposito %A Joel L. Lebowitz %A Rossana Marra %T Hydrodynamics of Binary Fluid Phase Segregation %D Dec 4, 2002 %Z Fri Dec 13 10:55:11 EDT 2002 %I DIMACS %R 2002-51 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-51.pdf %X Starting with the Vlasov-Boltzmann equation for a binary fluid mixture, we derive an equation for the velocity field u when the system is segregated into two phases (at low temperatures) with a sharp interface between them. u satisfies the incompressible Navier-Stokes equations together with a jump boundary condition for the pressure across the interface which, in turn, moves with a velocity given by the normal component of u. Numerical simulations of the Vlasov-Boltzmann equations for shear flows parallel and perpendicular to the interface in a phase segregated mixture support this analysis. We expect similar behavior in real fluid mixtures. %A Gabriela Alexe %A Sorin Alexe %A Yves Crama %A Stephan Foldes %A Peter L. Hammer %A Bruno Simeone %T Consensus algorithms for the generation of all maximal bicliques %D Dec 8, 2002 %Z Fri Dec 13 10:55:11 EDT 2002 %I DIMACS %R 2002-52 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-52.ps.gz %X We describe a new algorithm for generating all maximal bicliques (i.e. complete bipartite, not necessarily induced subgraphs) of a graph. The algorithm is inspired by, and is quite similar to, the consensus method used in propositional logic. We show that some variants of the algorithm are totally polynomial, and even incrementally polynomial. The total complexity of the most efficient variant of the algorithms presented here is polynomial in the input size, and only linear in the output size. Computational experiments demonstrate its high efficiency on randomly generated graphs with up to 2,000 vertices and 20,000 edges. %A Dieter Rautenbach %T A Note on Linear Discrepancy and Bandwidth %D Dec 8, 2002 %Z Fri Dec 13 10:55:12 EDT 2002 %I DIMACS %R 2002-53 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-53.ps.gz %X Fishburn, Tanenbaum and Trenk \cite{FTT01a} define the linear discrepancy ${\rm ld}(P)$ of a poset $P=(V,<_P)$ as the minimum integer $k\geq 0$ for which there exists a bijection $f:V\to\{ 1,2,\ldots,|V|\}$ such that $u<_P v$ implies $f(u) < f(v)$ and $u||_P v$ implies $|f(u)-f(v)|\leq k$. In \cite{FTT01b} they prove that the linear discrepancy of a poset equals the bandwidth of its cocomparability graph.

Here we provide partial solutions to some problems formulated in \cite{FTT01a} about the linear discrepancy and the bandwidth of cocomparability graphs. %A Vadim Lozin %A Dieter Rautenbach %T On the band-, tree- and clique-width of graphs with bounded vertex degree %D Dec 8, 2002 %Z Fri Dec 13 10:55:12 EDT 2002 %I DIMACS %R 2002-54 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-54.ps.gz %X The band-, tree- and clique-width are of primary importance in algorithmic graph theory due to the fact that many problems being NP-hard for general graphs can be solved in polynomial time when restricted to graphs where one of these parameters is bounded. It is known that for any fixed $\Delta\geq 3$, all three parameters are unbounded for graphs with vertex degree at most $\Delta$. In this paper, we distinguish representative subclasses of graphs with bounded vertex degree that have bounded band-, tree- or clique-width. Our proofs are constructive and lead to efficient algorithms for a variety of NP-hard graph problems when restricted to those classes. %A T. Laustsen %A F. Verstraete %A S. J. van Enk %T Local vs. joint measurements for the entanglement of assistance %D Dec 8, 2002 %Z Fri Dec 13 10:55:15 EDT 2002 %I DIMACS %R 2002-55 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-55.ps.gz %X We consider a variant of the entanglement of assistance, as independently introduced by D.P. DiVincenzo {\em et al.} ({\tt quant-ph/9803033}) and O. Cohen (Phys. Rev. Lett. {\bf 80}, 2493 (1998)). Instead of considering three-party states in which one of the parties, the assistant, performs a measurement such that the remaining two parties are left with on average as much entanglement as possible, we consider four-party states where two parties play the role of assistants. We answer several questions that arise naturally in this scenario, such as (i) how much more entanglement can be produced when the assistants are allowed to perform joint measurements, (ii) for what type of states are local measurements sufficient, (iii) is it necessary for the second assistant to know the measurement outcome of the first, and (iv) are projective measurements sufficient or are more general POVMs needed? %A Tongyin Liu %A Yanpei Liu %T On Generating Three-connected Planar Graphs %D Dec 8, 2002 %Z Fri Dec 13 10:55:15 EDT 2002 %I DIMACS %R 2002-56 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-56.ps.gz %X In this paper, a new method of generating three connected planar graphs in terms of generators is provided. Also it is shown that a planar graph is three connected planar graph if, and only if, it has a wheel or a pseudo-wheel as a generator. %A Ying Liu %T Lower bounds for the size of binary space partition of rectangles %D Dec 8, 2002 %Z Fri Dec 13 10:55:15 EDT 2002 %I DIMACS %R 2002-57 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-57.ps.gz %X Binary space partition (BSP) tree is one of the most popular data structures in computational geometry. We proved that the lower bound on the exact size of BSP trees for a set of $n$ isothetic rectangles in the plane is $2n-o(n)$ when the rectangles tile the underlying space, this closed the gap between the upper and lower bounds for this case. Also, in general, for a set of $n$ isothetic rectangles in the plane, we improved the lower bound from $\frac{9}{4}n-o(n)$ to $\frac{7}{3}n-o(n)$. %A D. Frank Hsu %A Jacob Shapiro %A Isak Taksa %T Methods of data fusion in information retrieval: rank vs. score combination %D Feb 3, 2003 %Z Fri Apr 18 15:56:00 EDT 2003 %I DIMACS %R 2002-58 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-58.doc.gz %X Combination of multiple evidences (multiple query formulations, multiple retrieval schemes or systems) has been shown (mostly experimentally) to be effective in data fusion in information retrieval. However, the question of why and how combination should be done still remains largely unanswered. In this paper, we provide a model for simulation and analysis in the study of data fusion in the information retrieval domain. A rank-score function is defined and the concept of a Cayley graph is used in the design and analysis of our framework. Our model and results have led to better understanding of the data fusion phenomena in the information retrieval domain. In particular, we have shown (analytically) and in simulation that combination using rank performs better than combination using score under certain conditions. %A E. Boros %A V. Gurvich %A Y. Liu %T Comparison of convex hulls and box hulls %D Jan 22, 2003 %Z Fri Apr 18 16:20:18 EDT 2003 %I DIMACS %R 2003-01 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-01.ps.gz %X A {\it convex hull} of a set of points $X$ is the minimal convex set containing $X$. A {\it box $B$} is an interval $B=\{\vx|\vx\in [\va, \vb], \va, \vb \in \R^n\}$. A {\it box hull} of a set of points $X$ is defined to be the minimal box containing $X$. Because both convex hulls and box hulls are closure operations of points, classical results for convex sets can naturally be extended for box hulls. We consider here the extensions of theorems by Carath\'{e}odory, Helly and Radon to box hulls and obtain exact results. %A Vincent Mousseau %A Lu\'is C. Dias %A Jos\'e R. Figueira %T On the Notion of Category Size in Multiple Criteria Sorting Models %D Jan 22, 2003 %Z Fri Apr 18 16:20:19 EDT 2003 %I DIMACS %R 2003-02 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-02.ps.gz %X We consider the Multiple Criteria Sorting Problem, that aims at assigning each alternative in a finite set $A$ to one of the predefined categories. We propose a new concept of category size that refers to ``{\it the proportion by which an evaluation vector corresponding to a realistic alternative is assigned to the category}''.

Sorting problems usually refer to absolute evaluation (the assignment of an alternative does not depend on the others), as opposed to ranking and choice problems in which the very purpose is to compare alternatives against each other. Considering constraints concerning category size lead to define a Constrained Sorting Problem which refers both to absolute and relative evaluation.

After identifying decision situations in which category size is useful for modelling purposes, this paper defines the concept of category size and proposes a way to compute the size of categories, even when the set of alternatives and/or the preference information is/are imprecisely known. We show how this notion can be used in a preference elicitation process. Finally, in order to illustrate the use of this concept, we propose a procedure to infer the values for preference parameters that accounts for specifications (provided by the DM) about the size of categories, in the context of the UTADIS sorting model. %A V. Lozin %A D. Rautenbach %T Chordal Bipartite Graphs of Bounded Tree- and Clique-width %D Jan 27, 2003 %Z Fri Apr 18 16:20:20 EDT 2003 %I DIMACS %R 2003-03 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-03.ps.gz %X A bipartite graph is chordal bipartite if every cycle of length at least six has a chord. In the class of chordal bipartite graphs the tree-width and the clique-width are unbounded.

Our main results are that chordal bipartite graphs of bounded vertex degree have bounded tree-width and that $k$-fork-free chordal bipartite graphs have bounded clique-width, where a $k$-fork is the graph arising from a $K_{1,k+1}$ by subdividing one edge once. This implies polynomial-time solvability for a variety of algorithmical problems for these graphs. %A Xuhui Ao %A Naftaly Minsky %T Flexible Regulation of Distributed Coalitions %D Feb 10, 2003 %Z Fri Apr 18 16:20:21 EDT 2003 %I DIMACS %R 2003-04 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-04.ps.gz %X There is a growing tendency for organizations to form coalitions in order to collaborate---by sharing some of their resources, or by coordinating some of their activities. The question addressed in this paper is: how should such coalitions be regulated?

Our approach to this question is based on the following definition of the governance of coalitions: A coalition C is a set {E1,E2,...,En} of enterprises, which interoperate under an ensemble of policies [Pc, {Pi}], where Pc is the coalition policy that governs the coalition as a whole, and Pi is the local policy of enterprise Ei (for each i), which governs its participation in the coalition. This means, in particular, that every interaction between an agent Xi of enterprise Ei and an agent Xj of Ej must comply with the local policies Pi and Pj, as well as with the coalition policy Pc.

We also require that the policy-ensemble [Pc, {Pi}] of a coalition would satisfy the following principle of flexibility: Each local policy Pi can be defined and changed independently of other local policies in this ensemble, and without any knowledge of them.

We will describe a regulatory mechanism for coalitions, which provides for efficient and decentralized enforcement of a wide range of policies that might govern a coalition, and which satisfies our principle of flexibility. %A Piotr Berman %A Paul Bertone %A Bhaskar DasGupta %A Mark Gerstein %A Ming-Yang Kao %A Michael Snyder %T Fast Optimal Genome Tiling with Applications to Microarray Design and Homology Search %D Feb 10, 2003 %Z Fri Apr 18 16:20:23 EDT 2003 %I DIMACS %R 2003-05 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-05.ps.gz %X In this paper we consider several variations of the following basic tiling problem: given a sequence of real numbers with two size bound parameters, we want to find a set of tiles of maximum total weight such that each tiles satisfies the size bounds. A solution to this problem is important to a number of computational biology applications such as selecting genomic DNA fragments for PCR-based amplicon microarrays and performing homology searches with long sequence queries. Our goal is to design efficient algorithms with linear or near-linear time and space in the normal range of parameter values for these problems. For this purpose, we first discuss the solution to a basic online interval maximum problem via a sliding window approach and show how to use this solution in a non-trivial manner for many of the tiling problems introduced. We also discuss NP-hardness results and approximation algorithms for generalizing our basic tiling problem to higher dimensions. Finally, computational results from applying our tiling algorithms to genomic sequences of five model eukaryotes are reported. %A Andras Prekopa %A Xiaoling Hou %T A Data Mining Problem in Stochastic Programming %D Mar 5, 2003 %Z Fri Apr 18 16:20:24 EDT 2003 %I DIMACS %R 2003-06 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-06.ps.gz %X In this paper we consider a linear programming problem where some or all technology coefficients are deterministic but their values are unknown. Samples are taken to estimate these coefficients and the problem is to determine the optimal sample sizes. If we replace the unknown coefficients by their estimations, then we obtain a random linear programming problem the optimum value of which is also random. We want to find sample sizes such that the confidence interval, created for the unknown deterministic optimum value, by the use of the samples, should cover it by a prescribed large probability, and, subject to this constraint, the total cost of sampling should be minimum. %A Xiaomin Chen %T On a Conjecture of Chvatal %D Mar 11, 2003 %Z Fri Apr 18 16:20:25 EDT 2003 %I DIMACS %R 2003-07 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-07.ps.gz %X The Sylvester-Gallai theorem asserts that every finite set $S$ of points in two-dimensional Euclidean space includes two points, $a$ and $b$, such that either there is no other point in $S$ is on the line $ab$, or the line $ab$ contains all the points in $S$. Recently, V. Chv\'{a}tal extended the notion of lines to arbitrary metric spaces and made a conjecture that generalizes the Sylvester-Gallai theorem. We prove this conjecture for subspaces of $\ell_1^2$, the two-dimensional space with the $\ell_1$-metric. %A Wen-Hua Ju %A David Madigan %A Steven L. Scott %T On Bayesian Learning of Sparse Classifiers %D Mar 20, 2003 %Z Fri Apr 18 16:20:26 EDT 2003 %I DIMACS %R 2003-08 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-08.ps.gz %X Figueiredo (2001) and Figueiredo and Jain (2001) described a particular sparseness-inducing Bayesian model for probit regression. For several standard datasets, they reported predictive performance for their model that was as a good as, or better than, previously reported results. This paper explores several aspects of the Figueiredo and Jain model in an attempt to better understand its performance. We modify the Figueiredo and Jain approach in three ways. First, we introduce an alternative prior distribution. Second, we propose a fully Bayesian MCMC learning algorithm. Third, we replace their kernel based classifier with a linear classfier. We measure the impact of these modifications on three publicly available test data sets. Preliminary results indicate that while each change can produce a noticeable impact on test error rates, no one approach dominates the others in all cases. %A Krishnan Kumaran %A Lijun Qian %T Uplink Scheduling in CDMA Packet-Data Systems %D Apr 4, 2003 %Z Fri Apr 18 16:20:27 EDT 2003 %I DIMACS %R 2003-09 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-09.ps.gz %X Uplink scheduling in wireless systems is gaining importance due to arising uplink intensive data services (ftp, image uploads etc.), which could be hampered by the currently in-built asymmetry in favor of the downlink. In this work, we propose and study algorithms for efficient uplink packet-data scheduling in a CDMA cell. The algorithms attempt to maximize system throughput under transmit power limitations on the mobiles assuming instantaneous knowledge of user queues and channels. However no channel statistics or traffic characterization is necessary. Apart from increasing throughput, the algorithms also improve fairness of service among users, hence reducing chances of buffer overflows for poorly located users.

The major observation arising from our analysis is that it is advantageous on the uplink to schedule ``strong'' users one-at-a-time, and ``weak'' users in larger groups. This contrasts with the downlink where one-at-a-time transmission for all users has shown to be the preferred mode in much previous work. Based on the optimal schedules, we propose less complex and more practical approximate methods, both of which offer significant performance improvement compared to one-at-a-time transmission, and the widely acclaimed {\em Proportional Fair} (PF) algorithm, in simulations. When queue content cannot be fed back, we propose a simple modification of PF, {\em Uplink PF} (UPF), that offers similar improvement. %A E. Boros %A V. Gurvich %T Perfect Graphs, Kernels, and Cores of Cooperative Games %D Apr 1, 2003 %Z Fri Apr 18 16:20:28 EDT 2003 %I DIMACS %R 2003-10 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-10.ps.gz %X A kernel in a directed graph is an independent set, which is reachable from each other vertex by an arc. A directed graph in which every induced subgraph has a kernel is called kernel-perfect. The existence of a kernel in directed graphs, and in particular, kernel-perfect orientations of undirected graphs is strongly related to perfect graphs, and has several applications in combinatorics and game theory. These and related results are the subject of this survey. Though some of these results are independent of the Strong Perfect Graph Conjecture, the recent solution of this conjecture and the efficient recognition of perfect graphs have several important implications, in particular in game theory.

Key words: kernel, kernel-solvable graphs, perfect graphs, normal hypergraphs, Strong Perfect Graph Conjecture, Berge-Duchet conjecture; cooperative games, coalition, stable family of coalitions, game form, effectivity function, stable effectivity functions, Scarf theorem. %A Graham Cormode %A S. Muthukrishnan %T Radial Histograms for Spatial Streams %D Apr 1, 2003 %Z Fri Apr 18 16:20:29 EDT 2003 %I DIMACS %R 2003-11 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-11.ps.gz %X Many data streams relate to geographic or spatial information such as the tracking of moving objects, or location-specific measurements and queries. While several techniques have been developed recently for processing numerical, text or XML streams, new techniques are needed to process spatial queries on streaming geometric data.

We propose a novel data structure, the Radial Histogram, to process streams including spatial data points. It allows a number of geometric aggregates involving the spread and extent of the points in the data streams---diameter, furthest neighbors, convex hulls---to be accurately estimated to arbitrary precision. By using multiple Radial Histograms for a set of given facilities, we can process data streams consisting of massive numbers of client points. We can then accurately estimate number of spatial aggregates involving relative placement of clients with respect to the facilities, including reverse nearest neighbors, spatial joins and more.

Radial histograms use very small space and are exceedingly simple to implement. Nevertheless, we prove that they guarantee accurate estimation for spatial aggregate queries mentioned above. An experimental evaluation shows them to perform very well in practice. %A I. E. Zverovich %A V. E. Zverovich %T Basic perfect graphs and their extensions %D Apr 1, 2003 %Z Fri Apr 18 16:20:30 EDT 2003 %I DIMACS %R 2003-12 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-12.ps.gz %X We characterize basic graphs introduced by Chudnovsky, Robertson, Seymour, and Thomas \cite{ChudnovskyRST} in terms of forbidden induced subgraphs. %The {\em GraphLab} software package \cite{Zverovich-GraphLab} %was used in our research. Then we apply Reducing Pseudopath Method of Zverovich \cite{ZverovichRRR14-2001} to find forbidden induced subgraphs the substitutional closure of the class of basic graphs, thus obtaining a characterization of a hereditary subclass of perfect graphs. %A Gary McGraw %T From the Ground Up: The DIMACS Software Security Workshop %D Apr 4, 2003 %Z Fri Apr 18 16:20:31 EDT 2003 %I DIMACS %R 2003-13 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-13.ps.gz %X The DIMACS Software Security Workshop %A Piotr Berman %A Bhaskar DasGupta and Ming-Yang Kao %T Tight Approximability Results for Test Set Problems in Bioinformatics %D Apr 11, 2003 %Z Fri Apr 18 16:20:32 EDT 2003 %I DIMACS %R 2003-14 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-14.ps.gz %X In this paper, we investigate several versions of a test set problem. In the simplest version, given a family of tests, viewed as subsets of the universe, we want to select the smallest subfamily that separates every two elements of the universe. We show that this problem is exactly as difficult to approximate as the set cover problem, up to a factor of 1 plus or minus o(1). The same holds for several more elaborate versions of the problem that have applications in bioinformatics; for example, in one version the universe consists of strings over a finite alphabet and each test checks the presence of a specific substring. We also show that if we allow to form tests as unions of the given tests, the problem has essentially the same level of computational intractability as graph coloring. %A Victoria Ungureanu %A Michael Katehakis %A Benjamin Melamed %T Towards an Efficient Cluster-based E-Commerce Server %D Apr 16, 2003 %Z Fri Apr 18 16:20:34 EDT 2003 %I DIMACS %R 2003-15 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-15.ps.gz %X Cluster-based server architecture combines combines good performance and low cost, and is commonly used for applications involving high volume traffic of requests. Essentially, a cluster-based server consists of a front-end dispatcher and several back-end servers. The dispatcher receives incoming requests, and then assigns them to back-end servers, which are responsible with request processing. The many benefits of cluster-based servers make them a good choice for e-commerce applications as well. However, applying this type of architecture to e-commerce applications is hindered by the fact that an e-commerce cluster has the additional task of validating requests, i.e. it has to verify that requests comply with contract terms. The problem is further complicated by the fact that contract terms may be expressed in terms of dynamic, mutable state. The problem we are addressing in this paper is how can e-commerce requests be assigned for processing so that load can be balanced among back-end servers and validation of requests can be done in a efficient manner.

To deal with this problem we propose that each stateful contracts is a-priori assigned to a back-end server, called the base of this contract, which is responsible for maintaining its state. The dispatcher assigns requests in the following manner. A request governed by a stateless contracts is assigned to the least loaded server. A requests governed by a stateful contract is assigned to its base whenever the base is not overloaded. If the base is heavily loaded, the dispatcher assigns the request to the least loaded server. Only, in the last case the back-end server needs to contact the base to retrieve the state. To enable a back-end server to detect when the state is needed, we propose a contract formulation that explicitly states the contract type. %A Victoria Ungureanu %A Phillip G. Bradford %A Michael Katehakis %A Benjamin Melamed %T Class-Dependent Assignment in Cluster-based Servers %D Apr 16, 2003 %Z Fri Apr 18 16:20:35 EDT 2003 %I DIMACS %R 2003-16 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-16.ps.gz %X A cluster-based server consists of a front-end dispatcher and several back-end servers. The dispatcher receives incoming requests, and then assigns them to back-end servers for processing. Our goal is to devise an assignment policy that has good response time performance, and is practical to implement in that the amount of information used by the dispatcher is relatively small, so that the attendant computation and communication overheads are low. In contrast to extant assignment policies that apply the same assignment policy to all incoming jobs, our approach calls for the dispatcher to classify incoming jobs as long or short, and then use class-dependent assignment policies. Specifically, we propose a policy, called CDA (Class Dependent Assignment), where short jobs are assigned Round-Robin as soon as they arrive, while long jobs are deferred and assigned only when a back-end server becomes idle. Furthermore, when processing a long job, a back-end server is not assigned any other jobs.

Our approach is motivated by empirical evidence suggesting that the sizes of files traveling on the Internet follow power-law distributions, where long jobs constituting a small fraction of all incoming jobs actually account for a large fraction of the overall load. To gauge the performance of the proposed policy, we exercised it on empirical data traces measured at Internet sites serving the 1998 World Cup. Since the assignment of long jobs incurs computational overhead as well as extra communication overhead, we studied the performance of CDA as a function of the fraction of jobs classified as long. Our study shows that classification of even a small fraction of jobs as long can have a profound impact on overall response time performance. More specifically, our experimental results show that if less than 3% of the jobs are classified as long, then CDA outperforms traditional policies, such as Round-Robin, by two orders of magnitude. From an implementation viewpoint, these results support our contention that CDA -based assignment is a practical policy combining low overhead and greatly improved performance. %A Endre Boros %A Khaled Elbassioni %A Vladimir Gurvich %A Leonid Khachiyan %T On the Complexity of Some Enumeration Problems for Matroids %D Apr 16, 2003 %Z Fri Apr 18 16:20:37 EDT 2003 %I DIMACS %R 2003-17 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-17.ps.gz %X We present an incremental polynomial-time algorithm for enumerating all circuits of a matroid or, more generally, all minimal spanning sets for a flat. We also show the NP-hardness of several related enumeration problems. %A Flip Korn %A S. Muthukrishnan %A Yunyue Zhu %T IPSOFACTO: A Visual Correlation Tool for Aggregate Network Traffic Data %D May 20, 2003 %Z Fri Jun 20 16:33:46 EDT 2003 %I DIMACS %R 2003-18 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-18.ps.gz %X IP network operators collect aggregate traffic statistics on network interfaces via the Simple Network Management Protocol (SNMP). This is part of routine network operations for most ISPs; it involves a large infrastructure with multiple network management stations polling information from all the network elements and collating a real time data feed. This demo will present a tool that manages the live SNMP data feed on a fully operational large ISP at industry scale. The tool primarily serves to study correlations in the network traffic, by providing a rich mix of ad-hoc querying based on a user-friendly correlation interface and as well as canned queries, based on the expertise of the network operators with field experience. The tool is called IPSOFACTO for {\em IP Stream-Oriented FAst Correlation for Traffic Overseeing}. %A Flip Korn %A S. Muthukrishnan %A Yunyue Zhu %T Checks and Balances: Monitoring Data Quality Problems in Network Traffic Databases %D June, 2003 %Z Tue Aug 26 12:19:46 EDT 2003 %I DIMACS %R 2003-19 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-19.ps.gz %X

Internet Service Providers (ISPs) use real-time data feeds of aggregated traffic in their network to support technical as well as business decisions. A fundamental difficulty with building decision support tools based on aggregated traffic data feeds is one of data quality. Data quality problems stem from network-specific issues (e.g., irregular polling caused by UDP packet drops and delays, topological mislabelings, etc.), and make it difficult to distinguish between artifacts and actual phenomena, rendering data analysis based on such data feeds ineffective.

In principle, traditional integrity constraints and triggers may be used to enforce data quality. In practice, data cleaning is done outside the database and is ad-hoc. Unfortunately, these approaches are too rigid or limited for the subtle data quality problems arising from network data where existing problems morph with network dynamics, new problems emerge over time, and poor quality data in a local region may itself indicate an important phenomenon in the underlying network. We need a new approach -- both in principle and in practice -- to face data quality problems in network traffic databases.

We propose a continuous data quality monitoring approach based on probabilistic, approximate constraints (PACs). These are simple, user-specified rule templates with open parameters for tolerance and likelihood. We rely on statistical techniques to derive effective parameter values from the data, and show how to apply them for monitoring data quality. In principle, our PAC-based approach can be applied to data quality problems in any data feed. We present PACMAN, which is the system that manages PACs for the entire aggregate network traffic database in a large ISP, and show that it is very effective in monitoring data quality problems.

%A Graham Cormode %A S. Muthukrishnan %T Improved Data Stream Summaries: The Count-Min Sketch and its Applications %D June, 2003 %Z Tue Aug 26 12:20:03 EDT 2003 %I DIMACS %R 2003-20 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-20.ps.gz %X We introduce a new small space data structure -- the Count-Min Sketch -- for summarizing data streams. Our sketch allows fundamental queries in data stream summarization such as point, range and inner product queries to be approximately answered quickly and efficiently; in addition it can eb applied to solve several important problems in data stream such as finding quantiles, frequent items, etc. In both cases, the time and space bounds we show using the CM sketch significantly improves those known for previous sketch constructions -- typically from 1/epsilon^2 to 1/epsilon in factor. %A Alexis Tsoukias %T From Decision Theory to Decision Aiding Methodology %D June, 2003 %Z Tue Aug 26 12:21:12 EDT 2003 %I DIMACS %R 2003-21 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-21.ps.gz %X The paper presents the author's partial and personal historical reconstruction of how decision theory evolved to decision aiding methodology. The presentation shows mainly how ``alternative'' approaches to classic decision theory evolved. In the paper is claimed that all such decision ``theories'' share a common methodological feature which is the use of formal and abstract languages as well as of a model of rationality. Different decision aiding approaches can thus be defined, depending on the origin of the model of rationality used in the decision aiding process. The concept of decision aiding process is then introduced and analysed. The paper ultimate claim is that all such approaches can be seen as part of a decision aiding methodology. %A I. E. Zverovich %T Independent domination on $2P_3$-free perfect graphs %D June, 2003 %Z Tue Aug 26 12:22:33 EDT 2003 %I DIMACS %R 2003-22 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-22.ps.gz %X We show that the independent domination problem is NP-complete for $2P_3$-free perfect graphs. %A Igor Zverovich %T A new kind of graph colorings %D June, 2003 %Z Tue Aug 26 12:23:13 EDT 2003 %I DIMACS %R 2003-24 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-24.ps.gz %X A proper k-coloring C1, C2, ..., Ck of a graph G is called strong if for every vertex u in V(G) there exists an index i in {1, 2, ..., k} such that u is adjacent to every vertex of Ci . We consider classes SCOLOR(k) of strongly k-colorable graphs and show that the recognition problem of SCOLOR(k) is NP-complete for every k >= 4, but it is polynomial-time solvable for k = 3. We give a characterization of SCOLOR(3) in terms of forbidden induced subgraphs. Finally, we solve the problem of uniqueness of a strong 3-coloring. %A Igor Zverovich %T On a problem of Lesniak, Polimeni, and Vanderjagt %D June, 2003 %Z Tue Aug 26 12:24:46 EDT 2003 %I DIMACS %R 2003-25 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-25.ps.gz %X We give almost complete solution to the following problem: for a fixed S, what is the minimum value p = uH (S) such that a pair (S; p) has a Hamiltonian realization? We give a criterion for a pair (S; p) to have a Hamiltonian realization. %A Igor Zverovich %T Algorithmic aspects of Reducing Pseudopath Method %D June, 2003 %Z Tue Aug 26 12:25:51 EDT 2003 %I DIMACS %R 2003-26 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-26.ps.gz %X

Let G and H be graphs. A substitution of H in G instead of a vertex v in V (G) is the graph G(v -> H), which consists of disjoint union of H and G - v with the additional edge-set {xy : x in V (H); y in NG (v)}. For a hereditary class of graphs P, the substitutional closure of P is defined as the class P* consisting of all graphs which can be obtained from graphs in P by repeated substitutions.

Let P be an arbitrary hereditary class for which a characterization in terms of forbidden induced subgraphs is known. Zverovich [20] proposed Reducing Pseudopath Method for constructing a forbidden induced subgraph characterization of P* . However, an implementation of the method is not straightforward.

We find conditions that guarantee the existence of a very simple reducing pseudopath [for example, of length 1]. As a result, a number of known and new characterizations may be obtained immediately by applying the improved method. In particular, we essentially simplify proofs given in Brandstadt, Hoang, and Zverovich [3]. As examples, we consider some interesting hereditary classes.

%A Kazuhisa Makino %A Yushi Uno %A Toshihide Ibaraki %T Minimum Edge Ranking Spanning Trees of Split Graphs %D June, 2003 %Z Tue Aug 26 12:27:12 EDT 2003 %I DIMACS %R 2003-27 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-27.ps.gz %X Given a graph $G$, the minimum edge ranking spanning tree problem (MERST) is to find a spanning tree of $G$ whose edge ranking is minimum. However, this problem is known to be NP-hard for general graphs. In this paper, we show that the problem MERST has a polynomial time algorithm for split graphs, which have useful applications in practice. The result is also significant in the sense that this is a first non-trivial graph class for which the problem MERST is found to be polynomially solvable. We also show that the problem MERST for threshold graphs can be solved in linear time, where threshold graphs are known to be split. %A Boros, Endre %A Gurvich, Vladimir %T Stable Effectivity Functions and Perfect Graphs %D January 7, 1999 %Z Mon, 20 Dec 1999 16:00:00 GMT %I DIMACS %R 99-01 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-01.ps.gz %X We consider the problem of characterizing the stability of effectivity functions (EFF), via a combinatorial correspondance between game theoretic and well-known combinatorial concepts. To every EFF we assign a pair of hypergraphs, representing clique covers of two associated graphs, and obtain some necessary and some sufficient conditions for the stability of EFFs in terms of graph-properties. These conditions imply e.g. that to check the stability of an EFF is an NP-complete problem. We also translate some well known conjectures of graph theory into game theoretic language and vice versa. %A Johannes E. Gehrke %A S. Muthukrishnan %A Rajmohan Rajaraman %A Anthony Shaheen %T Scheduling to Minimize Average Stretch %D January 13, 1999 %Z Fri, 26 Feb 1999 18:00:00 GMT %I DIMACS %R 99-02 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-02.ps.gz %X

We consider the classical problem of online preemptive job scheduling on uniprocessor and multiprocessor machines. For a given job, we measure the quality of service provided by an algorithm by the stretch of the job, which is defined as the ratio of the amount of time that the job spends in the system to the processing time of the job. For a given sequence of jobs, we measure the performance of an algorithm by the average stretch achieved by the algorithm over all the jobs in the sequence.

We first prove that no on-line algorithm can achieve a competitive ratio that is smaller than 1.03. The main contribution of this paper is to show that the shortest remaining processing time algorithm (SRPT) is O(1)-competitive with respect to average stretch for both uniprocessors as well as multiprocessors. For uniprocessors, we prove that SRPT is 2-competitive. We also establish an essentially matching lower bound on the competitve ratio of SRPT on uniprocessors. For multiprocessors, we show that the competitive ratio of SRPT is at most 14.

%A Ilya Muchnik %A Vadim Mottl %A Vladimir Levyant %T Massive Data Set Analysis in Seismic Explorations for Oil and Gas in Crystalline Basement Interval %D January 19, 1999 %Z Fri, 26 Feb 1999 18:00:00 GMT %I DIMACS %R 99-03 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-03.ps.gz %X On the basis of the optimization-based approach to the analysis of massive ordered data sets, a new method is proposed for computer-aided interpretation of seismic exploratory data from the so-called crystalline basement of the Earth mantle, which underlies the relatively thin sedimentary cover having been, up to now, the almost exceptional object of seismic explorations. The seismic exploratory data sets, seismic sections and cubes, are a class of, respectively, two- and three-dimensional data arrays, which are analyzed in the course of gas and oil reserves prospecting with the purpose of studying the structure of the underground rock mass. The seismic data sets consist of synchronous records of reflected seismic signals registered by a large number of geophones (seismic sensors) placed along a straight line or in the nodes of a rectangular lattice on the earth surface. As the source of the initial seismic pulse, usually serves a series of explosions, responses to which are averaged in a special manner. The vertical time axis forming the resulting two- or three-dimensional picture is identified with depth, so that the peculiarities of the reflected signal under the respective sensor carry an information on the local properties of the rock mass at the respective point of the underground medium. In contrast to the above-lying sedimentary cover, the absence of pronounced reflecting surfaces in a crystalline body results in a great difficulty of inferring the geological information from the basement interval of the seismic picture. The new method of seismic data analysis proposed in this work is aimed at finding fractured zones of the basement rock mass capable to accumulate oil or gas. The essence of the method consists in numerical evaluating distinctions in the local spatial texture of the seismic picture that are caused by differences in physical properties of fractured and monolith rock. The problem of estimating the local texture over the whole data array at once is set as that of minimizing an objective function in that the texture model parameters at all the elements of the array occur as its arguments. A special separable structure of the objective function provides a high speed of the optimization procedure. %A Avishai Wool %A Bulent Yener %T Combinatorial Design of Multi-Ring Networks with Combined Routing and Flow Control %D January 20, 1999 %Z Fri, 26 Feb 1999 18:00:00 GMT %I DIMACS %R 99-04 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-04.ps.gz %X

In this paper we present a novel design technique, and combined routing and flow control algorithms, for congestion-free packet switched networks.

The design is based on the construction of multiple virtual rings, under the constraint that the path between any two nodes is either confined to a single ring, or traverses exactly two rings (passing through a single bridge node).

Our best designs are constructed by using Finite Generalized Quadrangles of combinatorial design theory, together with a scaling algorithm for realizing networks of arbitrary size. The target topology is obtained by taking the edge union of the multiple virtual rings.

Capitalizing on the underlying topological properties, we design routing, flow and access control protocols. We prove that the proposed network architecture, coupled with our protocols, ensures that (i) no loss due to congestion occurs inside a network, under arbitrary traffic patterns; (ii) all the packets reach their destinations within bounded time; and (iii) the bandwidth is allocated fairly and no host is starved.

Moreover, we achieve these desirable properties much more efficiently than earlier proposals. Our best designs have a maximum route length of O(N^{1/3}) and require O(N^{1/3}) ports to be used at each node for an N-node network. The designs attain these bounds while manifesting a high degree of redundancy, with multiple disjoint paths between all pairs of nodes. This significantly improves upon the designs of [YOY94b,YOY98], where both the route length and number of ports are Omega(sqrt(N)), and only a single path exists between every pair of nodes.

We also provide a theoretical bound for the impact of fairness and congestion-freeness on netwok utilization. We used this design technique to generate network designs of various sizes. We then implemented our protocols and verified their performance by simulations.

%A A. Ashikhmin %A A. Barg %A S. Litsyn %T A New Upper Bound on Codes Decodable into Size-2 Lists %D January 21, 1999 %Z Tue, 30 Mar 1999 18:00:00 GMT %I DIMACS %R 99-05 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-05.ps.gz %X A new asymptotic upper bound on the size of binary codes with the property described in the title is derived. The proof relies on the properties of the distance distribution of binary codes established in earlier related works of the authors. %A A. Ashikhmin %A A. Barg %A S. Litsyn %T A New Upper Bound on the Reliability Function of the Gaussian Channel %D January 21, 1999 %Z Tue, 30 Mar 1999 18:00:00 GMT %I DIMACS %R 99-06 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-06.ps.gz %X

We derive a new upper bound on the exponent of error probability of decoding for the best possible codes in the Gaussian channel. This bound is tighter than the known upper bounds (the sphere-packing and minimum-distance bounds proved in Shannon's classical 1959 paper and their low-rate improvement by Kabatiansky and Levenshtein). The proof is accomplished by studying asymptotic properties of codes on the Euclidean $n$-dimensional sphere. First we prove that the distance distribution of codes of large size necessarily contains a large component. A general theorem establishing this estimate is proved simultaneously for codes on the Euclidean sphere and in real and complex projective spaces.

To derive specific estimates of the distance distribution, we study the asymptotic behavior of Jacobi polynomials $P_k^{\alpha,\beta}$ as $k\to \infty$ and at least one of the upper indices grows linearly in $k$. This group of results provides the exact behavior of the exponent of Jacobi polynomials in the entire orthogonality segment.

Since on the average there are many code vectors in the vicinity of the transmitted vector $\bfx$, one can show that the probability of confusing $\bfx$ and one of these vectors cannot be too small. This proves a lower bound on the error probability of decoding and the upper bound announced in the title.

%A Andrew Odlyzko %T The Internet and Other Networks: Utilization Rates and Their Implications %D January 21, 1999 %Z Tue, 30 Mar 1999 18:00:00 GMT %I DIMACS %R 99-07 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-07.ps.gz %X

Costs of communications networks are determined by the maximal capacities of those networks. On the other hand, the traffic those networks carry depends on how heavily those networks are used. Hence utilization rates and utilization patterns determine the costs of providing services, and therefore are crucial in understanding the economics of communications networks.

A comparison of utilization rates and costs of various networks helps disprove many popular myths about the Internet. Although packet networks are often extolled for the efficiency of their transport, it often costs more to send data over internal corporate networks than using modems on the switched voice network. Packet networks are growing explosively not because they utilize underlying transport capacity more efficiently, but because they provide much greater flexibility in offering new services.

Study of utilization patterns shows there are large opportunities for increasing the efficiency of data transport and making the Internet less expensive and more useful. On the other hand, many popular techniques, such as some Quality of Service measures and ATM, are likely to be of limited usefulness.

%A Andrew Odlyzko %T The Economics of the Internet: Utility, Utilization, Pricing, and Quality of Service %D January 21, 1999 %Z Tue, 30 Mar 1999 18:00:00 GMT %I DIMACS %R 99-08 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-08.ps.gz %X Can high quality be provided economically for all transmissions on the Internet? Current work assumes that it cannot, and concentrates on providing differentiated service levels. However, an examination of patterns of use and economics of data networks suggests that providing enough bandwidth for uniformly high quality transmission may be practical. If this turns out not to be possible, only the simplest schemes that require minimal involvement by end users and network administrators are likely to be accepted. On the other hand, there are substantial inefficiencies in the current data networks, inefficiencies that can be alleviated even without complicated pricing or network engineering systems. %A Andrew Odlyzko %T Smart and Stupid Networks: Why the Internet Is Like Microsoft %D January 21, 1999 %Z Tue, 30 Mar 1999 18:00:00 GMT %I DIMACS %R 99-09 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-09.ps.gz %X Is the Internet growing primarily because it is a dumb network, one that simply delivers packets from one point to another? Probably not. If were a dumb network, we surely would not need huge and rapidly growing ranks of network professionals. A more detailed look suggests that the Internet is succeeding largely for the same reasons that led the PC to dominate the mainframe, and are responsible for the success of Microsoft. Like the PC, the Internet offers an irresistible bargain to a crucial constituency, namely developers, while managing to conceal the burden it places on users. %A Andrew Odlyzko %T Data Networks are Lightly Utilized, and Will Stay That Way %D January 21, 1999 %Z Tue, 30 Mar 1999 18:00:00 GMT %I DIMACS %R 99-10 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-10.ps.gz %X The popular press often extolls packet networks as much more efficient than switched voice networks in utilizing transmission lines. This impression is reinforced by the delays experienced on the Internet and the famous graphs for traffic patterns through the major exchange points on the Internet, which suggest that networks are running at full capacity. This paper shows the popular impression is incorrect; data networks are very lightly utilized compared to the telephone network. Even the backbones of the Internet are run at lower fractions (10% to 15%) of their capacity than the switched voice network (which operates at over 30% of capacity on average). Private line networks are utilized far less intensively (at 3% to 5%). Further, this situation is likely to persist. The low utilization of data networks compared to voice phone networks is not a symptom of waste. It comes from different patterns of use, lumpy capacity of transmission facilities, and the high growth rate of the industry. %A K. G. Coffman %A Andrew Odlyzko %T The Size and Growth Rate of the Internet %D January 21, 1999 %Z Tue, 30 Mar 1999 18:00:00 GMT %I DIMACS %R 99-11 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-11.ps.gz %X The public Internet is currently far smaller, in both capacity and traffic, than the switched voice network. The private line networks are considerably larger in aggregate capacity than the Internet. They are about as large as the voice network in the U.S., but carry less traffic. On the other hand, the growth rate of traffic on the public Internet, while lower than is often cited, is still about 100% per year, much higher than for traffic on other networks. Hence, if present growth trends continue, data traffic in the U.S. will overtake voice traffic around the year 2002 and will be dominated by the Internet. %A Peter Fishburn %A Andrew Odlyzko %T Dynamic Behavior of Differential Pricing and Quality of Service Options for the Internet %D January 21, 1999 %Z Tue, 30 Mar 1999 18:00:00 GMT %I DIMACS %R 99-12 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-12.ps.gz %X

The simple model on which the Internet has operated, with all packets treated equally, and charges only for access links to the network, has contributed to its explosive growth. However, there is wide dissatisfaction with the delays and losses in current transmission. Further, new services such as packet telephony require assurance of considerably better service. These factors have stimulated the development of methods for providing Quality of Service (QoS), and this will make the Internet more complicated. Differential quality will also force differential pricing, and this will further increase the complexity of the system.

The solution of simply putting in more capacity is widely regarded as impractical. However, it appears that we are about to enter a period of rapidly declining transmission costs. The implications of such an environment are explored by considering models with two types of demands for data transport, differing in sensitivity to congestion. Three network configurations are considered: (1) with separate networks for the two types of traffic, (2) with a single network that provides uniformly high QoS, and (3) with a single physical network that provides differential QoS. The best solution depends on the assumptions made about demand and technological progress. However, we show that the provision of uniformly high QoS to all traffic may well be best in the long run. Even when it is not the least expensive, the additional costs it imposes are usually not large. In a dynamic environment of rapid growth in traffic and decreasing prices, these costs may well be worth paying to attain the simplicity of a single network that treats all packets equally and has a simple charging mechanism.

%A Jean-Claude Bermond %A Johny Bond %A Carole Martin %A Aleksandar Pekec %A Fred S. Roberts %T Optimal Orientations of Annular Networks %D February 10, 1999 %Z Tue, 30 Mar 1999 18:00:00 GMT %I DIMACS %R 99-13 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-13.ps.gz %X Annular Network $AN(c,s)$ is a graph representing a $c\times s$ grid in polar coordinates. We give lower bounds for the diameter of orientations of $AN(c,s)$ and provide orientations which show that bounds are tight in most cases. %A Abram Kagan %A Colin L. Mallows %A Larry A. Shepp %A Robert J. Vanderbei %A Yehuda Vardi %T Symmetrization of Binary Random Variables %D February 10, 1999 %Z Tue, 30 Mar 1999 18:00:00 GMT %I DIMACS %R 99-14 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-14.ps.gz %X A random variable $Y$ is called an independent symmetrizer of a given random variable $X$ if (a) it is independent of $X$ and (b) the distribution of $X+Y$ is symmetric about $0$. In cases where the distribution of $X$ is symmetric about its mean, it is easy to see that the constant random variable $Y = - \Exp X$ is a minimum-variance independent symmetrizer. Taking $Y$ to have the same distribution as $-X$ clearly produces a symmetric sum but it may not be of minimum variance. We say that a random variable $X$ is symmetry resistant if the variance of any symmetrizer, $Y$, is never smaller than the variance of $X$. Let $X$ be a binary random variable: $\Prob \{ X = a \} = p$ and $\Prob \{ X = b \} = q$ where $a \ne b$, $0 < p < 1$, and $q = 1-p$. We prove that such a binary random variable is symmetry resistant if (and only if) $p \ne 1/2$. Note that the minimum variance as a function of $p$ is discontinuous at $p = 1/2$. Dropping the independence assumption, we show that the minimum-variance reduces to $pq - \min (p,q)/2$, which is a continuous function of $p$. %A Julia Abrahams %T Addition Chains as Test Trees and a Sequential Variant as the Huffman Problem %D February 10, 1999 %Z Tue, 30 Mar 1999 18:00:00 GMT %I DIMACS %R 99-15 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-15.ps.gz %X An addition chain can be interpreted as a test tree to identify a single distinguished item from a set of candidates. In this diagnostic problem, there is a constant cost associated with setting up a test, distinct tests distinguish between different size subsets of items, and all tests are set up in advance. If the tests are set up sequentially as needed and if a probability is assigned to each item of its being the single item sought by the testing procedure, the Huffman algorithm finds the optimal test tree in the sense of minimizing the average cost of setting up the tests used in the testing procedure. %A Fred Roberts %A Shaoji Xue %T Characterizations of Consistent Marked Graphs %D March 4, 1999 %Z Tue, 30 Mar 1999 18:00:00 GMT %I DIMACS %R 99-16 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-16.ps.gz %X A marked graph is a graph with a + or - sign on each vertex and is called consistent if each cycle has an even number of - signs. This concept is motivated by problems of communication networks and social networks. We present some new characterizations/recognition algorithms for consistent marked graphs. %A Geza Toth %T Note on geometric graphs %D March 4, 1999 %Z Tue, 30 Mar 1999 18:00:00 GMT %I DIMACS %R 99-17 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-17.ps.gz %X A geometric graph is a graph drawn in the plane so that the vertices are represented by points in general position, the edges are represented by straight line segments connecting the corresponding points. We show that a geometric graph of $n$ vertices with no $k+1$ pairwise disjoint edges has at most $2^9k^2n$ edges. %A Li Sheng %A Jie Wu %T On Lower Bound of the Number of Channels for Deadlock-Free Whormhole Routing %D April 2, 1999 %Z Wed, 28 Mar 1999 23:00:00 GMT %I DIMACS %R 99-18 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-18.ps.gz %X Libeskind-Hadas recently provided a tight lower bound on the number of channels required by a broad class of deadlock-free wormhole routing algorithm. Given an interconnection network represented by a digraph $G=(N,C)$, where each vertex in $N$ represents a node and each directed link in $C$ represents a unidirectional channel, Libeskind-Hadas showed that $|C|\ge 2|N|-2$ is the tight lowered on the number of Channels required for Deadlock-Free Whormhole Routing. In this short note, we show a simpler proof of this tight lower bound. %A Jie Wu %A Li Sheng %T Deadlock-Free Routing in Irregular Networks Using Prefix Routing Algorithm %D April 2, 1999 %Z Wed, 28 Mar 1999 23:00:00 GMT %I DIMACS %R 99-19 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-19.ps.gz %X In this paper, we propose a deadlock-free routing in irregular networks using prefix routing. Prefix routing is a special type of routing with a compact routing table associated with each node (processor). Basically, each outgoing channel of a node is assigned a special label and an outgoing channel is selected if its label is a prefix of the label of the destination node. Node and channel labeling in an irregular network is done through constructing a spanning tree. The routing process follows a two-phase process of going up and then down along the spanning tree, with a possible cross channel (shortcut) between two branches of the tree between two phases. We show that the proposed routing scheme is deadlock- and livelock- free. %A Balakrishna Subramanian %A Ido Kanter %A Eytan Domany %A Joel Lebowitz %T Statistical Properties of Contact Maps %D April 12, 1999 %Z Wed, 28 Mar 1999 23:00:00 GMT %I DIMACS %R 99-20 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-20.ps.gz %X A contact map is a simple representation of the structure of proteins and other chain-like macromolecules. This representation is quite amenable to numerical studies of folding. We show that the number of contact maps corresponding to the possible configurations of a polypeptide chain of $N$ amino acids, represented by $(N-1)$-step self avoiding walks on a lattice, grows exponentially with $N$ for all dimensions $D > 1$. We carry out exact enumerations in $D=2$ on the square and triangular lattices for walks of up to 20 steps and investigate various statistical properties of contact maps corresponding to such walks.. We also study the exact statistics of contact maps generated by walks on a ladder. %A Balakrishna Subramanian %A Joel Lebowitz %T The study of three-body interaction Hamiltonian on a lattice %D April 12, 1999 %Z Wed, 28 Mar 1999 23:00:00 GMT %I DIMACS %R 99-21 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-21.ps.gz %X We investigate the phase diagram and the segregation kinetics of a system of particles with three-body interactions on a two dimensional square lattice. We compare this to the usual case of pair interactions which have particle-hole symmetry. Our simulations suggest that the kinetics belong to the same universality class as the symmetric model with pair interactions. %A Ahmed A.Belal %A Mohamed S.Selim %A Shymaa M.Arafat %T Towards a Dynamic Optimal Alphabetic Tree %D April 12, 1999 %Z Tue, 9 May 2000 20:00:00 GMT %I DIMACS %R 99-22 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-22.ps.gz %X

Optimal alphabetic binary trees have a wide variety of applications in computer science and information systems. Fast algorithms for building such trees in O(n log n) do exist. However, no existing algorithm makes it possible to insert in (or delete from) the tree without losing its optimality. In this paper, we propose an algorithm to insert into or delete from an optimal binary alphabetic tree in linear time keeping the tree optimal after insertion or deletion. We show that both insertion and deletion of a node can be done in O(n) time provided its weight is not bigger than the higher weight of its two neighbouring nodes. This algorithm makes it possible to have a dynamic optimal alphabetic tree with reasonable complexity and allows us to expand the domain of weight sequences whose optimal alphabetic trees can be obtained in linear time.

Key words: Optimal alphabetic tree, insertion and deletion, linear-time alphabetic trees.

%A Piotr Berman %A Marek Karpinski %T On Some Tighter Inapproximability Results %D April 23, 1999 %Z Fri, 21 May 1999 23:00:00 GMT %I DIMACS %R 99-23 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-23.ps.gz %X We give a number of improved inapproximability results, including the best up to date explicit approximation thresholds for bounded occurrence satisfiability problems like MAX-2SAT and E2-LIN-2, and the bounded degree graph problems, like MIS, NodeCover, and MAX CUT. We prove also for the first time inapproximability of the problem of Sorting by Reversals and display an explicit approximation threshold. %A Endre Boros %A Tonguc Unluyurt %T Sequential Testing of Series-Parallel Systems of Small Depth %D April 26, 1999 %Z Wed, 28 Mar 1999 23:00:00 GMT %I DIMACS %R 99-24 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-24.ps.gz %X We consider the problem of testing sequentially the components of a multi component system, when the testing of each component is costly. We consider a polynomial time testing policy for series-parallel systems, proposed in the literature. Generalizing published results, we prove that the considered policy is cost-minimal in the average case sense, for two sub-families of series-parallel systems. We also demonstrate via examples that neither this algorithm nor some of its improved versions are optimal for general series-parallel systems, disproving some published claims. %A Danny Raz %A Yuval Shavitt %T An Active Network Approach to Efficient Network Management %D May 5, 1999 %Z Thu, 22 Jul 1999 23:50:00 GMT %I DIMACS %R 99-25 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-25.ps.gz %X

Active networks is a framework where network elements, primarily routers and switches, are programmable. Programs that are injected into the network are executed by the network elements to achieve higher flexibility and to present new capabilities.

This work describes a novel active network architecture which primarily addresses the management challenges of modern complex networks. Its primary component is an active engine that is attached to any IP router to form an active node. The active engine we designed and implemented executes programs that arrive from the network and monitors and controls the router actions. The design is based on standards (Java, SNMP, ANEP over UDP), and can be easily deployed in todays IP networks.

The contribution of this paper is the introduction of novel architectural features such as: isolation of the active mechanism, the session concept, the ability of active session to control non-active packets, and blind addressing. Implementing these ideas, we built a system that enables the safe execution and rapid deployment of new distributed management applications in the network layer. This system can be gradually integrated in todays IP networks, and allows smooth migration from IP to active networking.

%A Hans van Maaren %T A Short Note on Linear Autarkies, q-Horn Formulas and the Complexity Index %D May 7, 1999 %Z Fri, 21 May 1999 23:00:00 GMT %I DIMACS %R 99-26 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-26.ps.gz %X It is shown that the tractable class of CNF formulas solvable by Linear Autarkies properly contains the class of q-Horn formulas and that it is incomparable with SLUR. %A Greg Perkins %A Diane Souvaine %T Efficient Radio Wave Propagation for Wireless Radio Signal Prediction %D May 28, 1999 %Z Mon, 21 Jun 1999 21:00:00 GMT %I DIMACS %R 99-27 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-27.ps.gz %X

Due to the ever increasing complexity of wireless network design,  wireless network simulation engines have become a necessary tool for wireless network engineers. A signal-strength prediction system lies at the foundation of every wireless simulator, making signal-strength prediction for microcells and picocells an important research topic in the radio field. Efficient and accurate methods are needed for use in current wireless network design and future wireless network research.

This paper describes a system, PREDICT, designed for use in wireless radio signal prediction research. PREDICT tracks the expansion of a transmitter's wavefront by modeling the wavefront as an ever expanding sphere centered upon the transmitter. The sphere's expansion is tracked by discretizing the sphere's surface with a triangulation and then propagating each triangular wavefront through the environment. In the propagation prediction of these triangular wave fronts, PREDICT supports reflection, transmission and diffraction based upon the geometric optics (GO) model of electromagnetic waves. Signal prediction is performed through a special summation of the predicted multi-path at a receiver.

PREDICT's algorithms have been specifically designed for use in radio signal prediction. The current environments supported by PREDICT are urban with flat or varied terrain and a single floor of a building, where all obstacles in the environment have vertical or horizontal walls. The system design is flexible, allowing PREDICT to be expanded for use in many different environments. Modularity allows for easy modification to the GO model or implementation of alternate radio modeling methods (one can easily modify PREDICT, or use the results generated by PREDICT, with one's own radio wave modeling methods). PREDICT is publicaly available for any non-commercial use.

%A E. Boros %A V. Gurvich %T On Parallel Edges in Cycles %D June 2, 1999 %Z Mon, 21 Jun 1999 21:00:00 GMT %I DIMACS %R 99-28 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-28.ps.gz %X Let $n\leq N$ be positive integers. We consider the problem of finding an $n$-cycle with no parallel edges in a perfect $N$-gon in the Euclidian plane. We prove that there exist no such $n$-cycle if and only if $N=n$ and even. And we show by construction that for every other pair $(N,n)$, $N \geq n \geq 3$, such an $n$-cycle exists. %A V. Gurvich %A Li Sheng %T Camel Sequences and Their Applications %D June 2, 1999 %Z Mon, 21 Jun 1999 21:00:00 GMT %I DIMACS %R 99-29 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-29.ps.gz %X

Given an even cyclic (0,1) sequence $s = (s_1,..., s_{2n})$ which consists of $n$ ones and $n$ zeros, let us compute $i + j (mod 2n)$ for all $n^2$ (0,1)-pairs $(s_i,s_j)$ and distribute obtained $n^2$ numbers between $2n$ "boxes" $1,2,...,2n-1,2n=0 (mod 2n)$. Obviously, the average cardinality of a box is $\frac{n^2}{2n}=\frac{n}{2}$. The following five sequences have quite remarcable box-distributions, "almost average everywhere with two big humps":

$n=3$, $s = (110100)$, $B = (112113) = (1^2 \, 2 \, 1^2 \, 3)$;

$n=7$, $s = (11101000110100)$, $B = (33333363333337) = (3^6 \, 6 \, 3^6 \, 7)$;

$n=11$, $s = (1110001001011100010110)$, $B = (5^{10} \, 10 \; 5^{10} \, 11)$;

$n=5$, $s = (1110010100)$, $B = (3333133330) = (3^4 \, 1 \, 3^4 \, 0)$;

$n=17$, $s = (1111101000110001011011010001100010)$, $B = (9^{16} \, 1 \, 9^{16} \, 0)$.

In general, given an {\em odd} $n$, box-distributions $(\lfloor\frac{n}{2}\rfloor^{n-1} (n-1) \lfloor\frac{n}{2}\rfloor^{n-1} n)$ and $(\lceil\frac{n}{2}\rceil^{n-1} \; 1 \lceil\frac{n}{2}\rceil^{n-1} \; 0)$ as well as the generating sequences will be called the {\em camel distributions} and the {\em camel sequences}, respectively {\em up-camel} and {\em down-camel}. We conjecture that there are infinitely many of them, both types, though only five are known. The first three sequences above are up-camel, and the last two are down-camel. We consider some applications of camel sequences in extremal graph theory.

Key Words: (0,1)-sequence, camel sequence, maximin, minimax, extremal graph theory, vertex-enumerated graphs

%A Endre Boros %A Toshihide Ibaraki %A Kazuhisa Makino %T Fully Consistent Extensions of Partially Defined Boolean Functions with Missing Bits %D June 2, 1999 %Z Sun, 27 Jun 1999 23:00:00 GMT %I DIMACS %R 99-30 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-30.ps.gz %X In this paper we consider four different definitions for an extension of a partially defined Boolean function in which the input contains some missing bits. We show that, for many general and reasonable families of function classes, three of these extensions are mathematically equivalent. However we also demonstrate that such an equivalence does not hold for all classes. %A E. Boros %A V. Gurvich %A S. Hougardy %T Recursive Generation of Partitionable Graphs %D June 7, 1999 %Z Sun, 27 Jun 1999 23:00:00 GMT %I DIMACS %R 99-31 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-31.ps.gz %X Results of Lov\'asz (1972) and Padberg (1974) imply that partitionable graphs contain all the potential counterexamples to Berge's famous Strong Perfect Graph Conjecture. A recursive method of generating partitionable graphs was suggested by Chv\'atal, Graham, Perold and Whitesides (1979). Results of Seb\H{o} (1996) entail that Berge's conjecture holds for all the partitionable graphs obtained by this method. Here we suggest a more general recursion. Computer experiments show that it generates {\em all} the partitionable graphs with $\go = 3, \ga \leq 9$ (we conjecture that the same will hold for bigger $\ga$, too) and 'almost all' for $(\go,\ga) = (4,4)$ and $(4,5)$. Here $\ga$ and $\go$ are respectively the clique and stability numbers of a partitionable graph, i.e. numbers of vertices in its maximum clique and stable set. All the partitionable graphs generated by our method contain a {\em critical $\go$-clique}, that is an $\go$-clique which intersects only $2\go-2$ other $\go$-cliques. This property might imply that in our class there are no counterexamples to Berge's conjecture (c.f. Seb\H{o} (1996)), however this question is still open. %A Boris Galitsky %T Natural Language Understanding with the Generality Feedback %D June 10, 1999 %Z Sun, 27 Jun 1999 23:00:00 GMT %I DIMACS %R 99-32 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-32.ps.gz %X

This study addresses the problem of improving the quality of natural language (NL) understanding by means of the involvement of the additional criterion of correct formal representation of the input inquiry. This criterion is based on the logical compatibility between the input inquiry, translated into the formal language, and the domain, encoded in the same language. Inquiry generality is measured as a normalized number of object tuples, which deliver the translation satisfaction for a given domain. Computational experiments in various domains show that the certain diapason of generality indicates the proper translation. Specific heuristics are developed for the transformation of the translation formula to improve the value of the generality criterion.

Usually, if the generality is too high (there is a large number of the tuples of objects) then the semantic analyzer has likely ignored some syntactic constraints for the translation formula. On the contrary, when the generality is too low (there is no object tuples, satisfying the translation), then the semantic analyzer has likely introduced too many syntactic constraints, and some of them have to be eliminated.

Generality criterion helps in the frequent situations, where the morphological and syntactic processing is insufficient for the construction of the proper inquiry translation into the formal language. Our approach is based on the experimentally verified fact that the user poses inquiries with the reasonable generality. This knowledge helps us to improve the semantic analysis to function in the flexible and expandable domains, where the lexical information is rather limited.

Compatibility feedback by means of generality control poses the specific requirements to the formal language of inquiry translation and domain knowledge representation. The semantic processor is implemented as a logical program with metalanguage support to present the complex semantic rules. Suggested approach allowed us to build the NL understanding system with high inquiry complexity, involving up to 3-4 concepts.

%A Markus Jakobsson %A Ari Juels %T Millimix: Mixing in Small Batches %D June 10, 1999 %Z Thu, 22 Jul 1999 23:50:00 GMT %I DIMACS %R 99-33 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-33.ps.gz %X We present Millimix, a mix network that is highly efficient on small input batches. The construction is conceptually simple, and both robust and private in the face of collusion by any minority set of malicious players. Additionally, Millimix the feature of being publicly verifiable. In other words, the mixing operation yields a transcript that demonstrates correctness to a third party that the mix proceeded correctly. %A Michael Saks %A Aravind Srinivasan %A Shiyu Zhou %A David Zuckerman %T Low Discrepancy Sets Yield Approximate Min-Wise Independent Permutation Families %D October 24, 1999 %Z Wed, 27 Oct 1999 21:00:00 GMT %I DIMACS %R 99-34 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-34.ps.gz %X Motivated by a problem of filtering near-duplicate Web documents, Broder, Charikar, Frieze \& Mitzenmacher defined the following notion of {\em $\epsilon$-approximate min-wise independent permutation families}. A multiset ${\cal F}$ of permutations of $\{0,1,\ldots,n-1\}$ is such a family if for all $K \subseteq \{0,1,\ldots,n-1\}$ and any $x \in K$, a permutation $\pi$ chosen uniformly at random from ${\cal F}$ satisfies $$|\ \Pr[\min\{\pi(K)\}=\pi(x)]-{1\over |K|}\ |\le{\eps\over |K|}.$$ We show connections of such families with {\em low discrepancy sets for geometric rectangles}, and give explicit constructions of such families ${\cal F}$ of size $n^{O(\sqrt{\log n})}$ for $\eps=1/n^{\Theta(1)}$, improving upon the previously best-known bound of Indyk. We also present polynomial-size constructions when the min-wise condition is required only for $|K| \le 2^{O(\log^{2/3} n)}$, with $\epsilon \geq 2^{-O(\log^{2/3} n)}$. %A Aleksandar Pekec %A Fred S. Roberts %T The Role Assignment Model Nearly Fits Most Social Networks %D June 11, 1999 %Z Thu, 22 Jul 1999 23:50:00 GMT %I DIMACS %R 99-35 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-35.ps.gz %X Role assignments, introduced by Everett and Borgatti \cite{Everett91}, who called them role colorings, formalize the idea, arising in the theory of social networks, that individuals of the same social role will relate in the same way to individuals playing counterpart roles. If $G$ is a graph, a $k${\em -role assignment} is a surjective function mapping each vertex into a positive integer $1,2,\ldots,k$, so that if $x$ and $y$ have the same role, then the sets of roles assigned to their neighbors are the same. We show that all graphs $G$ having no astronomical discrepancies between the minimum and the maximum degree have a $k$-role assignment. Furthermore, we introduce and study a natural measure expressing how close an onto map $f:V(G)\rightarrow\{1,\ldots, k\}$ is to being a $k$-role assignment of a graph $G=(V,E)$, and show that almost all graphs nearly have a $k$-role assignment. %A Marek Karpinski %T Randomized Complexity of Linear Arrangements and Polyhedra %D June 12, 1999 %Z Thu, 22 Jul 1999 23:50:00 GMT %I DIMACS %R 99-36 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-36.ps.gz %X We survey some of the recent results on the complexity of recognizing n-dimensional linear arrangements and convex polyhedra by randomized algebraic decision trees. We give also a number of concrete applications of these results. In particular, we derive first nontrivial, in fact quadratic, randomized lower bounds on the problems like Knapsack and Bounded Integer Programming. We formulate further several open problems and possible directions for future research. %A Janos Pach %A Joel Spencer %A Geza Toth %T New Bounds on Crossing Numbers %D June 21, 1999 %Z Thu, 22 Jul 1999 23:50:00 GMT %I DIMACS %R 99-37 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-37.ps.gz %X

The crossing number, ${\mbox {cr}}(G)$, of a graph $G$ is the least number of crossing points in any drawing of $G$ in the plane. Denote by $\kappa(n,e)$ the minimum of ${\mbox {cr}}(G)$ taken over all graphs with $n$ vertices and at least $e$ edges. We prove a conjecture of P. Erd\H os and R. Guy by showing that $\kappa(n,e)n^2/e^3$ tends to a positive constant as $n\rightarrow\infty$ and $n\ll e\ll n^2$. Similar results hold for graph drawings on any other surface of fixed genus.

We prove better bounds for graphs satisfying some monotone properties. In particular, we show that if $G$ is a graph with $n$ vertices and $e\ge 4n$ edges, which does not contain a cycle of length four (resp. six), then its crossing number is at least $ce^4/n^3$ (resp. $ce^5/n^4$), where $c>0$ is a suitable constant. These results cannot be improved, apart from the value of the constant. This settles a question of M. Simonovits.

%A P.G. Kevrekidis %A C.K.R.T. Jones %T Bifurcation of Internal Solitary Wave Modes from the Essential Spectrum %D June 27, 1999 %Z Thu, 22 Jul 1999 23:50:00 GMT %I DIMACS %R 99-38 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-38.ps.gz %X The bifurcation of internal modes from the phonon band in models supporting solitary wave solutions has been one of the exciting new phenomena in the field. We will present a number of analytical and semi-analytical techniques for the detection, study and understanding of these modes. We will see how they appear, without threshold, due to the discretization of the continuum equations. This perturbation is viewed in terms of a singular continuum approximation and analyzed by both perturbation theory and the Evans' function method. It is shown that these methods give equivalent results. Moreover, they are corroborated by mixed analytical-numerical computations based on the discrete Evans' function recently developed by the first author. The extent to which these predictions survive to strong discretizations are discussed. The results will be presented in the context of both the sine-Gordon and the $\phi^4$ models. %A Meena Mahajan %A P. R. Subramanya %A V. Vinay %T A Combinatorial Algorithm for Pfaffians %D July 9, 1999 %Z Thu, 22 Jul 1999 23:50:00 GMT %I DIMACS %R 99-39 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-39.ps.gz %X

The Pfaffian of an oriented graph is closely linked to Perfect Matching. It is also naturally related to the determinant of an appropriately defined matrix. This relation between Pfaffian and determinant is usually exploited to give a fast algorithm for computing Pfaffians.

We present the first completely combinatorial algorithm for computing the Pfaffian in polynomial time. Our algorithm works over arbitrary commutative rings. Over integers, we show that it can be computed in the complexity class GapL; this result was not known before. Our proof techniques generalize the recent Mahajan-Vinay combinatorial characterization of determinant in novel ways.

As a corollary, we show that under reasonable encodings of a planar graph, Kasteleyn's algorithm for counting the number of perfect matchings in a planar graph is also in GapL. The combinatorial characterization of Pfaffian also makes it possible to directly establish several algorithmic and complexity theoretic results on Perfect Matching which otherwise use determinants in a roundabout way.

We also present hardness results for computing the Pfaffian of an integer skew-symmetric matrix. We show that this is hard for #L and GapL under logspace many-one reductions.

Keywords: pfaffian, perfect matchings, determinant, planar graphs, GapL

%A V. Gurvich %A Li Sheng %T Camel Sequences and Quadratic Residues %D July 12, 1999 %Z Thu, 22 Jul 1999 23:50:00 GMT %I DIMACS %R 99-40 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-40.ps.gz %X

Given an even cyclic $(+1,-1)$ sequence $s = (s_0,..., s_{2n-1})$ which consists of $n$ plus ones and $n$ minus ones, let us compute $i + j \ (mod\ 2n)$ for all $n^2$ $(+1,-1)$-pairs $(s_i,s_j)$ and distribute obtained $n^2$ numbers between $2n$ "boxes" $1,2,...,2n-1,2n=0 \ (mod\ 2n)$. The average cardinality of a box is $\frac{n^2}{2n}=\frac{n}{2}$. Some sequences have quite remarkable box-distributions, "almost average everywhere with two big humps". For example,

$n=5, s = (+1+1-1-1+1-1+1-1-1+1),\ B = (3333133330) = (3^4 1 \, 3^4 0)\ $

$n=7, s = (+1+1+1-1+1-1-1-1+1+1-1+1-1-1),\ B = (33333363333337) = (3^6 6 \, 3^6 7)$.

In general, given an {\em odd} $n$, the box-distributions $(\lfloor\frac{n}{2}\rfloor^{n-1} \ (n-1) \\lfloor\frac{n}{2}\rfloor^{n-1} \ n)$ and $(\lceil\frac{n}{2}\rceil^{n-1} \ 1 \ \lceil\frac{n}{2}\rceil^{n-1} \ 0)$ as well as the sequences, which generate them, will be called the {\em camel distributions} and {\em camel sequences}, respectively {\em up-camel} and {\em down-camel}. For example, the first sequence above is down-camel, and the second one is up-camel. Camel sequences have applications in extremal graph theory. Here we prove that there are infinitely many 'camels' of both types. More precisely, for every prime $n=4j-1$ we construct an up-camel sequence and for every prime $n=4j+1$ a down-camel one. In both cases these sequences are related to quadratic residues and non-residues modulo $n$. We conjecture that there are no other camel sequences.

Key Words: quadratic residues, camel sequences, maximin, minimax, extremal graph theory, vertex-enumerated graphs.

%A Kazuhisa Makino %A Tiko Kameda %T Transformation of Regular Non-Dominated Coteries %D July 22, 1999 %Z Thu, 22 Jul 1999 23:50:00 GMT %I DIMACS %R 99-41 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-41.ps.gz %X

A coterie is a family of subsets such that every pair of subsets has at least one element in common but neither is a subset of the other.

A coterie $C$ is said to be non-dominated (ND) if there is no other coterie $D$ such that, for $\forall Q \in C$, there exists $Q' \in D$ satisfying $Q' \subseteq Q$.

We introduce an operator $\sigma$, which transforms a ND coterie to another ND coterie. A regular coterie is a natural generalization of a ``vote-assignable" coterie, which is used in some practical applications. We show that any ``regular" ND coterie $C$ can be transformed to any other regular ND coterie $D$ by judiciously applying $\sigma$ operations to $C$ at most $|C|+|D|-2$ times.

As another application of the $\sigma$ operation, we present an incrementally-polynomial-time algorithm for generating all regular ND coteries. We then introduce the concept of ``g-regular" function, as a generalization of availability. We show how to construct an optimum coterie $C$ with respect to a g-regular function in $O(n^3|C|)$ time. We also discuss the structures of optimum coteries with respect to a g-regular function.

%A Peter Fratzl %A Oliver Penrose %A Joel L. Lebowitz %T Modelling of Phase Separation in Alloys with Coherent Elastic Misfit %D July 30, 1999 %Z Mon, 2 Aug 1999 19:50:00 GMT %I DIMACS %R 99-42 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-42.ps.gz %X Elastic interactions arising from a difference of lattice spacing between two coherent phases can have a strong influence on the phase separation (coarsening) behaviour of alloys. If the elastic moduli are different in the two phases, the elastic interactions may accelerate, slow down or even stop the phase separation process. If the material is elastically anisotropic, the precipitates can be shaped like plates or needles instead of spheres and can \sps arrange themselves into highly correlated patterns \cs. Tensions or compressions applied externally to the specimen may have a strong effect on the shapes and arrangement of the precipitates. In this paper, we review the main theoretical approaches that have been used to model these effects and we relate them to experimental observations. The theoretical approaches considered are (i) `macroscopic' models treating the two phases as elastic media separated by a sharp interface (ii) `mesoscopic' models in which the concentration varies continuously across the interface (iii) `microscopic' models which use the positions of individual atoms. %A Tiina Heikkinen %T A Minimax Game of Power Control in a Wireless Network under Incomplete Information %D August 9, 1999 %Z Wed, 11 Aug 1999 23:50:00 GMT %I DIMACS %R 99-43 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-43.ps.gz %X The purpose of this paper is to study optimal transmit power control and capacity of a wireless multimedia network, where there is incomplete information about the link gain coefficients. Previously, Perron-Frobenius theory has been applied to the study of optimal power control under complete information about the link gain matrix and the interference matrix. This paper derives a characterization of optimal power vector and capacity in terms of an incomplete-information-matrix-game against nature choosing the elements of the link gain and interference matrices. A game theoretical rationale for not using power control is given. %A E. G. Coffman %A George S. Lueker %A Joel Spencer %A Peter M. Winkler %T Packing Random Rectangles %D September 2, 1999 %Z Wed, 27 Oct 1999 21:00:00 GMT %I DIMACS %R 99-44 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-44.ps.gz %X A random rectangle is the product of two independent random intervals, each being the interval between two random points drawn independently and uniformly from [0,1]. We prove that the number of items in a maximum cardinality disjoint subset of n random rectangles has the tight asymptotic bound Theta(n^{1/2}). Although tight bounds for the problem generalized to d>2 dimensions remain an open problem, we are able to show that Omega(n^{1/2}) and O((n log^{d-1}n)^{1/2}) are asymptotic lower and upper bounds. In addition, we prove that Theta(n^{d/(d+1)}) is a tight asymptotic bound for the case of random cubes. %A Paul A. Dreyer %A Xuerong Yong %T The Adjacency Matrix and Spectrum of a Graph with Negative Third Largest Eigenvalue %D September 13, 1999 %Z Wed, 27 Oct 1999 21:00:00 GMT %I DIMACS %R 99-45 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-45.ps.gz %X

Let $G$ be a simple connected graph with $n$ vertices, let $\lambda_i(G)$ be the $i$th largest eigenvalue of $G$. This paper provides the following results:

1. If $\lambda_3(G)<0$, then the adjacency matrix of $G$, $A(G)$ is cogredient to the matrix:

where $a_{ij}=1$ iff $i\ne j$ and $a_{ij}=0$ otherwise, and $$l_1+l_2+\ldots+l_k\le l.$$ Furthermore, if there exists an index $i$ such that $l_i > 1$, then $ G $ has the eigenvalue $-1$ with multiplicity at least $n-2r-1$, where $2r$ is the rank of $A(G^c)$.

2. $\lambda_3(G)<0 $ implies that $ \lambda_j(G)\ge -1$, $j=3,4,\ldots,n-r $, where $2r$ is the rank of the adjacency matrix of the complement of $G$, $2r \le n-1$.

%A Paul A. Dreyer %A Christopher Malon %A Jaroslav Nesetril %T Universal H-colorable Graphs Without A Given Configuration %D September 13, 1999 %Z Wed, 27 Oct 1999 21:00:00 GMT %I DIMACS %R 99-46 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-46.ps.gz %X

For every pair of finite connected graphs $F$ and $H$, and every integer $k$, we construct a universal graph $U$ with the following properties:

\begin{enumerate} \item There is a homomorphism $\pi :U \ra H$, but no homomorphism from $F$ to $U$. \item For every graph $G$ with maximal degree no more than $k$ having a homomorphism $h:G \ra H$, but no homomorphism from $F$ to $G$, there is a homomorphism $\alpha :G \ra U$, such that $h = \pi \circ \alpha$. \end{enumerate}

Particularly, this solves a problem regarding the chromatic number of a universal graph.

%A Bernardo Abrego %A Silvia Fernandez-Merchant %T On the Maximum Number of Equilateral Triangles II %D September 15, 1999 %Z Wed, 27 Oct 1999 21:00:00 GMT %I DIMACS %R 99-47 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-47.ps.gz %X Erdös and Purdy raised the problem of finding the maximum number of equilateral triangles determined by a set of $n$ points in ${\Bbb R}^{d}$. This question is investigated in the first part of this series. Here we study some variations where the sets in consideration are in convex or general position. Non trivial bounds are given for these problems, as well as for the corresponding questions where the triangles at issue have unit length side. %A Harry Buhrman %A Steve Fenner %A Lance Fortnow %A Dieter van Melkebeek %T Optimal Proof Systems and Sparse Sets %D September 17, 1999 %Z Wed, 27 Oct 1999 21:00:00 GMT %I DIMACS %R 99-48 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-48.ps.gz %X

We exhibit a relativized world where the class of sparse NP sets has no complete sets. This gives the first relativized world where no optimal proof systems exist.

We also examine under what reductions the class of sparse NP sets can have complete sets. We show a close connection between these issues and reductions from sparse to tally sets. We also consider the question as to whether the sparse NP sets have a computable enumeration.

%A Bhaskar DasGupta %A Georg Schnitger %T On the Computational Power of Analog Neural Networks %D October 8, 1999 %Z Wed, 27 Oct 1999 21:00:00 GMT %I DIMACS %R 99-49 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-49.ps.gz %X We survey the computational power of analog neural networks. %A Gabriela Hristescu %A Martin Farach-Colton %T Cluster-preserving Embedding of Proteins %D October 8, 1999 %Z Wed, 27 Oct 1999 21:00:00 GMT %I DIMACS %R 99-50 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-50.ps.gz %X

Similarity searching in protein sequence databases is a standard technique for biologists dealing with a newly sequenced protein. Exhaustive search in such databases is prohibitive because of the large sizes of these database and because pairwise comparisons are slow. Heuristic techniques, such as FASTA and BLAST, are useful because they are fast and accurate, though it has been shown that exhaustive search is more accurate. Therefore, there are times when one would like to perform an exhaustive search.

We propose an efficient method, called SparseMap, for preprocessing a database of proteins to support efficient similarity searches using expensive but sensitive distance functions, such as those based on Smith-Waterman similarity. Our method is based on a Low-dimensional Euclidean Embedding approach. We compare our method with other embedding approaches, and show that our method is faster and produces embeddings which preserve more biological information about the proteins, such as pairwise distance and biological clusters.

%A P.G. Kevrekidis %A M.I. Weinstein %T Dynamics of Lattice Kinks %D October 9, 1999 %Z Wed, 27 Oct 1999 21:00:00 GMT %I DIMACS %R 99-51 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-51.ps.gz %X

We consider a class of Hamiltonian nonlinear wave equations governing a field defined on a spatially discrete one dimensional lattice, with discreteness parameter, $d=h^{-1}$, where $h>0$ is the lattice spacing. The specific cases we consider in detail are the discrete sine-Gordon (SG) and discrete $\phi^4$ models. For finite $d$ and in the continuum limit ($d\to\infty$) these equations have static kink-like (heteroclinic) states which are stable. In contrast to the continuum case, due to the breaking of Lorentz invariance, discrete kinks cannot be ``Lorentz boosted" to obtain traveling discrete kinks. Peyrard and Kruskal pioneered the study of how a kink, initially propagating in the lattice dynamically adjusts in the absence of an available family of traveling kinks. We study in detail the final stages of the discrete kink's evolution during which it is pinned to a specified lattice site (equilibrium position in the Peierls-Nabarro barrier). We find:

(i) for $d$ sufficiently large (sufficiently small lattice spacing), the state of the system approaches an asymptotically stable ground state static kink (centered between lattice sites).

(ii) for $d$ sufficiently small $d

For discrete SG and discrete $\phi^4$ we have: wobbling kinks which have the same spatial symmetry as the static kink as well as ``g-wobblers'' and ``e-wobblers'', which have different spatial symmetry.

The large time limit of solutions with initial data near a kink is marked by damped oscillation about one of these two types of asymptotic states. In case (i) we compute the characteristics of the damped oscillation (frequency and $d$- dependent rate of decay). In case (ii) we prove the existence of, and give analytical and numerical evidence for the asymptotic stability of wobbling solutions.

The mechanism for decay is the radiation of excess energy, stored in {\it internal modes}, away from the kink core to infinity. This process is studied in detail using general techniques of scattering theory and normal forms. In particular, we derive a {\it dispersive normal form}, from which one can anticipate the character of the dynamics. The methods we use are very general and are appropriate for the study of dynamical systems which may be viewed as a system of discrete oscillators ({\it e.g.} kink together with its {\it internal modes}) coupled to a field ({\it e.g.} dispersive radiation or phonons). The approach is based on and extends an approach of one of the authors (MIW) and A. Soffer in previous work. Changes in the character of the dynamics, as $d$ varies, are manifested in topological changes in the phase portrait of the normal form. These changes are due to changes in the types of resonances which occur among the discrete internal modes and the continuum radiation modes, as $d$ varies.

Though derived from a time-reversible dynamical system, this normal form has a dissipative character. The dissipation is of an internal nature, and corresponds to the transfer of energy from the discrete to continuum radiation modes. The coefficients which characterize the time scale of damping (or {\it lifetime} of the internal mode oscillations) are a nonlinear analogue of ``Fermi's golden rule", which arises in the theory of spontaneous emission in quantum physics.

%A Piotr Berman %A Bhaskar DasGupta %T Improvements in Throughput Maximization for Real-Time Scheduling %D October 11, 1999 %Z Wed, 27 Oct 1999 21:00:00 GMT %I DIMACS %R 99-52 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-52.ps.gz %X We consider the problem of off-line throughput maximization for job scheduling on one or more machines, where each job has a release time, a deadline and a profit. Most of the versions of the problem discussed here were already treated by Bar-Noy et al.(Proc. 31st ACM STOC, 622-631, 1999). Our main contribution is to provide algorithms that do not use linear programming, are simple and much faster than the corresponding ones proposed in Bar-Noy et al., while either having the same quality of approximation or improving it. More precisely, compared to the results of in Bar-Noy et al., our pseudo-polynomial algorithm for multiple unrelated machines and all of our strongly-polynomial algorithms have better performance ratios, all of our algorithms run much faster, are combinatorial in nature and avoid linear programming. Finally, we show that algorithms with better performance ratios than 2 are possible if the stretch factors of the jobs are bounded. %A Adrian Dumitrescu %A Geza Toth %T Ramsey-type Results for Unions of Comparability Graphs %D October 25, 1999 %Z Wed, 27 Oct 1999 21:00:00 GMT %I DIMACS %R 99-53 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-53.ps.gz %X It is well known that the comparability graph of any partially ordered set of $n$ elements contains either a clique or an independent set of size at least $\sqrt{n}$. In this note we show that any graph of $n$ vertices which is the union of two comparability graphs on the same vertex set, contains either a clique or an independent set of size at least $n^{1 \over 3}$. On the other hand, there exist such graphs for which the size of any clique or independent set is at most $n^{0.4118}$. Similar results are obtained for graphs which are unions of a fixed number $k$ comparability graphs. We also show that the same bounds hold for unions of perfect graphs. %A Alexander Barg %T On Polynomial Invariants of Codes, Matroids and Finite Interaction Models %D October 28, 1999 %Z Wed, 10 Nov 1999 21:00:00 GMT %I DIMACS %R 99-54 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-54.ps.gz %X

A linear code can be thought of as a vector matroid represented by the columns of code's generator matrix; a well-known result in this context is Greene's theorem on a connection of the weight polynomial of the code and the Tutte polynomial of the matroid. We examine this connection from the coding-theoretic viewpoint, building upon the rank polynomial of the code. This enables us

%A Vadim Mottl %A Alexander Blinov %A Norman Zabusky %A Ilya Muchnik %T Apparent Motion in Spatial Time-varying Data: A Variational Approach to Pointwise Tracking of Coherent Structures in Computational Fluid Dynamics %D November 8, 1999 %Z Wed, 15 Dec 1999 02:00:00 GMT %I DIMACS %R 99-55 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-55.ps.gz %X By a massive time-varying data set is meant an experimentally acquired or mathematically simulated function of spatial coordinates and time which is to be analyzed with the purpose of studying behavior of the respective distributed dynamical system. We address here primarily problems of computational fluid dynamics that are concerned with the necessity to visualize and study overwhelming time-varying data sets generated by numerical unsteady simulations. Of a major interest is time tracking of persistent coherent structures of the fluid flow that use to arise, move in space for a time while, fade, and be replaced by new pattern building up from their remains. The spatial motion of persistent patterns in a time-varying data set is called here apparent motion because it does not coincide, in the general case, with mechanical motion of any physical particles. With the purpose of tracking coherent structures, it is proposed to evaluate the apparent motion in terms of apparent velocity of space points. The apparent velocity is to be estimated in the form of a time-varying vector field as result of processing the original time-varying data set or immediately in the course of numerical simulating the respective physical reality as solution of an additional system of partial differential equations. In both versions, we lean upon the variational approach to the analysis of massive data sets and estimate the vector field of apparent velocity as time-varying function that delivers the minimum value to a quadratic functional. In experiments with simulated two-dimensional time-varying spatial dynamics of the fluid's density and vorticity in shock wave interaction with an elliptical bubble, the estimated apparent velocity provided long-term pointwise tracking of persistent coherent structures. %A Weiwu Fang %A Fred S. Roberts %A Zhengrong Ma %T An Approach of Information Theory to Multiple Sequence Comparison %D November 8, 1999 %Z Wed, 15 Dec 1999 02:00:00 GMT %I DIMACS %R 99-56 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-56.ps.gz %X

Multiple sequence comparison is a basic problem for molecular biology and other sciences. In this paper, we introduce the concept of complete information set and some measurement principles for measuring multiple sequence discrepancy. Based on them, we present a new measurement method satisfying the principles for comparing multiple sequences. We show that this method can effectively distinguish different random sequences or DNA sequences, for example, distinguish DNA sequences of length 8000 by comparisons of 6-8 symbol strings or protein sequences of length 8000 by comparisons of 3-4 strings. It can also measure slight changes of a sequence, e.g., insertion or deletion of a symbol. We apply it in the study of molecular evolution; the results show that there is a hierarchic relationship among the cytochrome C protein sequences of different species, much as that in taxonomy; moreover, these results are consistent with previous studies.

Key Words: multiple sequence comparison, entropy, DNA, measurement

%A Stefan Langerman %A William Steiger %T An Optimal Algorithm for Hyperplane Depth in the Plane %D November 19, 1999 %Z Wed, 15 Dec 1999 02:00:00 GMT %I DIMACS %R 99-57 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-57.ps.gz %X Given a set of $n$ hyperplanes $h_1,\ldots,h_n \in R^d$ the hyperplane depth of a point $P\in R^d$ is the minimum number of hyperplanes that a ray from $P$ can meet. The {\em hyperplane depth} of the arrangement is the maximal depth of points $P$ not in any $h_i$. We give an optimal $O(n\log{n})$ deterministic algorithm to compute the hyperplane depth of an arrangement in dimension $d=2$. %A Bela Csaba %A Ali Shokoufandeh %A Endre Szemeredi %T Proof of a Conjecture of Bollobás and Eldridge for Graphs with Maximum Degree 3 %D November 22, 1999 %Z Wed, 15 Dec 1999 02:00:00 GMT %I DIMACS %R 99-58 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-58.ps.gz %X Let $G_1$ and $G_2$ be graphs on $n$ vertices. If there are edge-disjoint copies of $G_1$ and $G_2$ in $K_n$, then we say there is a packing of $G_1$ and $G_2$. A conjecture of Bollob\'as and Eldridge ~\cite{be78} asserts that, if $(\Delta(G_1)+1)(\Delta(G_2)+1)\le n+1$ then there is a packing of $G_1$ and $G_2$. We prove this conjecture when $\Delta(G_1)=3$, for sufficiently large $n$. %A Bela Csaba %T Note on the Work Function Algorithm %D November 24, 1999 %Z Wed, 15 Dec 1999 02:00:00 GMT %I DIMACS %R 99-59 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-59.ps.gz %X We prove that the work function algorithm is $(n-1)$-competitive for the $k$-server problem, where $n$ is the number of points in the metric space. This gives improved upper bounds when $k+3 \leq n \leq 2k-1$; in particular, it shows that the work function algorithm is optimal for $k=n-1$. %A Bhaskar DasGupta %A Barbara Hammer %T Hardness of Approximation of the Loading Problem for Multi-layered Feedforward Neural Nets %D November 29, 1999 %Z Wed, 15 Dec 1999 02:00:00 GMT %I DIMACS %R 99-60 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-60.ps.gz %X

In this paper we deal with the problem of efficient learning of feedforward neural networks. First, we consider the case when the objective is to maximize the ratio r of the correctly classified points compared to all points in a training set. We show that, for an arbitrary multilayered threshold network with varying input dimension and with a constant n_1 >= 2 neurons in the first hidden layer, it is NP-hard to approximate r within a relative error of at most \varepsilon=1/(68 n_1 2^{n_1}+ 136 n_1^3+ 136 n_1^2 +170n_1). If n_1 >= 3, then the above result is true with \varepsilon=c(n_1-1)/(5n_1^3+2n_1^32^{n_1}+4n_1^5+4n_1^4) for some positive constant c, even if restricted to situations where a solution without any misclassifications exists. Restricted to architectures with only one hidden layer and two hidden neurons approximation of r with relative error at most 1/c is NP-hard even if either (a) c=2244, the threshold activation function in the hidden layer is substituted by the classical sigmoid function, and the situation of \epsilon-separation of the output classification is assumed, or (b) c=2380 and the threshold activation function is substituted by the semilinear activation function commonly used in the neural net literature. For a single hidden layer threshold network with varying input dimension and k hidden nodes, approximating r within a relative error of at most c/k^5, for some positive constant c, is NP-hard even if restricted to situations where the number of examples is at most k^4. Finally, we consider the case when the objective is to minimize the failure ratio f in the presence of missclassification errors. We show that it is NP-hard to approximate f within any constant c>1 for a multilayered threshold network if the input biases are fixed to zero.

%A Myung Ho Kim %T A Geometric Model of Information Retrieval Systems %D December 7, 1999 %Z Wed, 15 Dec 1999 02:00:00 GMT %I DIMACS %R 99-61 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-61.ps.gz %X This decade has seen a great deal of progress in the development of information retrieval systems. Unfortunately, we still lack a systematic understanding of the behavior of the systems and their relationship with documents. In this paper we present a completely new approach towards the understanding of the information retrieval systems. Recently, it has been observed that retrieval systems in TREC 6 show some remarkable patterns in retrieving relevant documents. Based on the TREC 6 observations, we introduce a geometric linear model of information retrieval systems. We then apply the model to predict the number of relevant documents by the retrieval systems. The model is also scalable to a much larger data set. Although the model is developed based on the TREC 6 routing test data, I believe it can be readily applicable to other information retrieval systems. In Appendix, we explained a simple and efficient way of making a better system from the existing systems. %A Edre Boros %A Vladimir Gurvich %A Leonid Khachiyan %A Kazuhise Makino %T Dual-Bounded Hypergraphs: Generating Partial and Multiple Transversals %D December 11, 1999 %Z Thu, 16 Dec 1999 03:00:00 GMT %I DIMACS %R 99-62 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-62.ps.gz %X We consider two natural generalizations of the notion of transversal to a finite hypergraph, so called {\em multiple} and {\em partial} transversals. We show that the hypergraphs of all multiple and all partial transversals are dual-bounded in the sense that in both cases, the size of the dual hypergraph is bounded by a polynomial in the cardinality and the length of description of the input hypergraph. Our bounds are based on new inequalities of extremal set theory and threshold Boolean logic, which may be of independent interest. We also show that the problems of generating all multiple and all partial transversals for a given hypergraph are polynomial-time reducible to the generation of all ordinary transversals for another hypergraph, i.e., to the well-known dualization problem for hypergraphs. As a corollary, we obtain incremental quasi-polynomial-time algorithms for both of the above problems, as well as for the generation of all the minimal Boolean solutions for an arbitrary monotone system of linear inequalities. %A Edre Boros %A Martin Golumbic %A Vadim Levit %T On the Number of Vertices Belonging to all Maximum Stable Sets of a Graph %D December 21, 1999 %Z Wed, 2 Feb 2000 23:00:00 GMT %I DIMACS %R 99-63 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1999/99-63.ps.gz %X Let us denote by $\alpha (G)$ the size of a maximum stable set, and by $\mu(G)$ the size of a maximum matching of a graph $G$, and let $\xi (G)$ be the number of vertices which belong to all maximum stable sets. We shall show that $\xi (G)\geq 1+\alpha (G)-\mu (G)$ holds for any connected graph, whenever $\alpha(G)>\mu(G)$. This inequality improves on related results by Hammer, Hansen and Simeone (1982) and by Levit and Mandrescu (1998). We also prove that on the one hand, $\xi (G)>0$ can be recognized in polynomial time whenever $\mu (G)<\left| V\left( G\right)\right|/3$, and on the other hand that determining whether $\xi (G)>k$ is, in general, NP-complete for any fixed $k\geq 0$. %A Boros, Endre %A Hammer, Peter L. %A Ricca, Frederica %A Simeone, Bruno %T Closed Sets and Generators in Ternary Hamming Spaces %D January 15, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-01 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-01.ps.gz %X

The $n$-dimensional ternary Hamming space is $\TT^n$, where $\TT=\{ 0,1,2\}$. Three points in $\TT^n$ form a line if they have in common exactly $n-1$ components. A subset of $\TT^n$ is closed if, whenever it contains two points of a line, it contains also the third one. A generator is a set, whose closure is $\TT^n$. In this paper, we investigate several properties of closed sets and generators. Two alternative proofs of our main result, stating that the minimum cardinality of a generator is $2^n$, are provided.

The present study was motivated by some combinatorial questions concerning origin-destination matrices in transportation systems. %A Boros, Endre %A Hammer, Peter L. %A Ricca, Frederica %A Simeone, Bruno %T On the Complexity of Generation in Ternary Hamming Spaces %D January 15, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-02 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-02.ps.gz %X In this paper, a follow-up of DIMACS Report 98-01, we continue to study ternary Hamming spaces $\TT^n$, where $\TT=\{0,1,2\}$, and their generators. In particular, we are interested in the computational complexity of the generation of all vectors with respect to a specific generator $G\subseteq \TT^n$. We consider several parameters, i.e., depth and load, which provide alternative ways to measure the computational effort required in order to generate all points of $\TT^n$ starting from those of $G$. We establish lower and upper bounds on the minimum depth and the minimum load for a generator in, and prove that some of them are sharp. %A Boros, Endre %A Hammer, Peter L. %A Minoux, Michel %A Rader, David %T Optimal Cell Flipping to Minimize Channel Density in VLSI Design and Pseudo-Boolean Optimization %D January 16, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-03 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-03.ps.gz %X Cell flipping in VLSI design is an operation in which some of the cells are replaced with their ``mirror images'' with respect to a vertical axis, while keeping them in the same slot. After the placement of all the cells, one can apply cell flipping in order to further decrease the total area, approximating this objective by minimizing total wire length, channel width, etc. However, finding an optimal set of cells to be flipped is usually a difficult problem. In this paper we show that cell flipping can be efficiently applied to minimize channel density in the standard cell technology. We show that an optimal flipping pattern can be found in $O(p(\frac{n}{c})^{c})$ time, where $n$, $p$ and $c$ denote the number of nets, pins and channels, respectively. Moreover, in the one channel case (i.e. when $c=1$) the cell flipping problem can be solved in $O(p\log n)$ time. For the multi-channel case we present both an exact enumeration scheme and a mixed-integer program that generates an approximate solution very quickly. We present computational results on examples up to 139 channels and 65 000 cells. %A Steffen, Eckhard %T Measurements of Uncolorability %D January 16, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-04 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-04.ps.gz %X

A snark is a cubic bridgeless graph with chromatic index $\chi'=4$. These graph are also called uncolorable. We introduce parameters measuring the uncolorability of those graphs and relate them to each other.

For $k=2,3$ let $c_i$ be the maximum size of a $k$-colorable subgraph of a cubic graph $G=(V,E)$. We consider $r_3 = |E|-c_3$ and $r_2 = \frac{2}{3}|E| - c_2$. We show that on one side $r_3$ and $r_2$ bound each other, but on the other side that the difference between them can be arbitrarily large.

We also compare them to the oddness $\omega$ of $G$, the smallest possible number of odd circuits in a 2-factor of $G$. We construct cyclically 5-edge connected graphs where $r_3$ and $\omega$ arbitrarily far apart, and show that for each $1 \leq c < 2$ there is a snark such that $\omega \geq c r_3$.

For $k=2,3$ let $\zeta_k$ denote the largest fraction of edges that can be edge $k$-colored. We give best possible bounds for these parameters, and relate them to each other. %A Desper, Richard %T The Set-Maxima Problem, an Overview %D January 19, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-05 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-05.ps.gz %X

Sorting problems have long been one of the foundations of theoretical computer science. Sorting problems attempt to learn properties of an unknown total order of a known set. We test the order by comparing pairs of elements, and through repeated tests deduce some order structure on the set.

The set-maxima problem is: given a family S of subsets of a set X, produce the maximal element of each element of S. Local sorting is a sub-problem of set-maxima, when S is a subset of (X (choose) 2), i.e. there exists a graph G with vertex set X and edge set S. We compare algorithms by estimating the number of comparisons needed, as a function of n = |X|, and m = |S|.

In this paper, we review the information-theory lower bounds for the set-maxima and local-sorting problems. We review deterministic algorithms which have optimally solved the set-maxima problem, as a function of m,n, in settings where extra assumptions about S have been made. Also, we review randomized algorithms for local sorting and set-maxima which achieve an optimal expected number of comparisons. %A Wool, Avishai %T Key Management for Encrypted Broadcast %D January 21, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-06 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-06.ps.gz %X

We consider broadcast applications where the transmissions need to be encrypted, such as broadband digital TV networks or Internet multicasts. In these applications the number of encrypted TV programs may be very large, but the secure memory capacity at the set-top terminals (STT) is severely limited due to the need to withstand pirate attacks and hardware tampering. Despite this, we would like to allow the vendor to offer different packages of programs to the users. A user who buys a package should be able to view every program belonging to that package, but nothing else. A flexible scheme should allow for packages of various sizes to be offered, from a single program up to all the programs.

We suggest a novel scheme to manage the encryption keys for these applications. The scheme is highly flexible, yet requires very few keys to be stored in the STTs' secure memory. The computational power required of the STTs is very low. The security of this scheme is as good or better than that offered by current technology. %A Jansen, Klaus %T A Characterization for Parity Graphs and a Coloring Problem with Costs %D January 29, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-07 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-07.ps.gz %X

In this paper, we give a characterization for parity graphs. A graph is a parity graph, if and only if for every pair of vertices all minimal chains joining them have the same parity. We prove that $G$ is a parity graph, if and only if the cartesian product $G \times K_2$ is a perfect graph.

Furthermore, as a consequence we get a result for the polyhedron corresponding to an integer linear program formulation of a coloring problem with costs. For the case that the costs $k_{v,3} = k_{v,c}$ for each color $c \ge 3$ and vertex $v \in V$, we show that the polyhedron contains only integral $0 / 1$ extrema if and only if the graph $G$ is a parity graph. %A Jansen, Klaus %T The Mutual Exclusion Scheduling Problem for Permutation and Comparability Graphs %D January 29, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-08 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-08.ps.gz %X In this paper, we consider the mutual exclusion scheduling problem for comparability graphs. Given an undirected graph $G$ and a fixed constant $m$, the problem is to find a minimum coloring of $G$ such that each color is used at most $m$ times. The complexity of this problem for comparability graphs was mentioned as an open problem by M\"ohring (1985) and for permutation graphs (a subclass of comparability graphs) as an open problem by Lonc (1991). We prove that this problem is already NP-complete for permutation graphs and for each fixed constant $m \ge 6$. %A Ekin, Oya %A Hammer, Peter L. %A Kogan, Alexander %T Convexity and Logical Analysis of Data %D February 2, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-09 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-09.ps.gz %X A Boolean function is called $k$-convex if for any pair $x,y$ of its true points at Hamming distance at most $k$, every point ``between'' $x$ and $y$ is also true. Given a set of true points and a set of false points, the central question of Logical Analysis of Data is the study of those Boolean functions whose values agree with those of the given points. In this paper we examine data sets which admit $k$-convex Boolean extensions. We provide polynomial algorithms for finding a $k$-convex extension, if any, and for finding the maximum $k$ for which a $k$-convex extension exists. We study the problem of uniqueness, and provide a polynomial algorithm for checking whether all $k$-convex extensions agree in a point outside the given data set. We estimate the number of $k$-convex Boolean functions, and show that for small $k$ this number is doubly exponential. On the other hand, we also show that for large $k$ the class of $k$-convex Boolean functions is PAC-learnable. %A Goldwasser, Michael H. %T Patience is a Virtue: The Effect of Delay on Competitiveness for Admission Control %D February 4, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-10 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-10.ps.gz %X

We consider the problem of scheduling a single resource non-preemptively in order to maximize its utilization. The delay of a job is equal to the gap between its arrival time and the last possible time at which it may be started while still meeting its deadline. We introduce an additional restriction that each job must be willing to accept a delay proportional to its job length. That is, we assume there is some constant w, such that any job of length |J| allows a delay of at least w|J|. This restriction is quite natural for admission control, as it seems reasonable that a job requesting 5 minutes of a resource might be willing to wait at least 10 seconds before beginning if necessary, whereas a job requesting 5 hours of time should be willing to handle a wait of 10 minutes instead.

Our results show that this additional requirement has dramatic effects on the competitiveness of online algorithms. Without this restriction, previous lower bounds show that no algorithm, deterministic or randomized, can achieve any bounded competitiveness for the problem when arbitrarily job lengths are allowed. We show that for any w>0 a simple greedy algorithm is (2 + 1/w)-competitive, and we give lower bounds showing that this is the best possible result for a deterministic algorithm, even when all jobs have one of three distinct lengths. In the special case where all jobs have the same length, previous results give a tight bound of 2 on the competitiveness for deterministic algorithms without a minimum delay. We generalize these results, showing that the competitiveness for any w>0 is exactly 1 + 1/(floor(w)+1). We also give tight bounds for the case where jobs have one of two distinct lengths. %A Abrahams, Julia %T Nonexhaustive Generalized Fibonacci Trees in Unequal Costs Coding Problems %D February 13, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-11 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-11.ps.gz %X In a sequence of generalized Fibonacci trees, the k-th tree has the (k-c(i))-th tree as its i-th subtree for a nondecreasing sequence of positive integers c(i), i=1,...,r. For particular initializations, each tree in the generalized Fibonacci sequence solves a minimax coding problem related to Varn coding. Specifically, each symbol from a uniformly distributed source is to be encoded by a string of code symbols associated with the path through the tree from the root to the leaf associated with the source symbol, the i-th code symbol costs c(i), and the goal is to minimize maximum codeword cost. %A Sheng, Li %A Wang, Chi %A Zhang, Peisen %T Tagged Probe Interval Graphs %D February 13, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-12 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-12.ps.gz %X A generalization of interval graph is introduced for cosmid contig mapping of DNA. A graph is a tagged probe interval graph if its vertex set can be partitioned into two subsets of probes and nonprobes, and a closed interval can be assigned to each vertex such that two vertices are adjacent if and only if at least one of them is a probe and one end of its corresponding interval is contained in the interval corresponding to the other vertex. We show that tagged probe interval graphs are weakly triangulated graphs, hence are perfect graphs. For a tagged probe interval graph with a given partition, we give a chordal completion that is consistent to any tagged interval completions with respect to the same vertex partition. Forbidden induced subgraph lists are given for trees with or without a given vertex partition. A heuristic that construct map candidates is given for cosmid contig mapping. %A Thomas, Simon %A Velickovic, Boban %T On the Complexity of the Isomorphism Relation for Finitely Generated Groups %D February 18, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-13 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-13.ps.gz %X Working within the framework of descriptive set theory, we show that the isomorphism relation for finitely generated groups is a universal essentially countable Borel equivalence relation. We also prove the corresponding result for the conjugacy relation for subgroups of the free group on two generators. The proofs are group-theoretic, and we refer to descriptive set theory only for the relevant definitions and for motivation for the results. %A Awerbuch, Baruch %A Shavitt, Yuval %T Topology Aggregation for Directed Graph %D February 23, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-14 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-14.ps.gz %X This paper addresses the problem of aggregating the topology of a sub-network in a compact way with minimum distortion. The problem arises from networks that have a hierarchical structure, where each sub-network must advertise the cost of routing between each pair of its border nodes. The straight-forward solution of advertising the exact cost for each pair has a quadratic cost which is not practical. We look at the realistic scenario of networks where all links are bidirectional, but their cost (or distance) in the opposite directions might differ significantly.

The paper present a solution with distortion that is bounded by the logarithm of the number of border nodes and the square-root of the asymmetry in the cost of a link. This is the first time that a theoretical bound is given to an undirected graph. We show how to apply our solution to the ATM PNNI standard. %A Muchnik, Ilya %A Mottl, Vadim %T Bellman Functions on Trees for Segmentation, Generalized Smoothing, Matching Multi-Alignment in Massive Data Sets %D February 25, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-15 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-15.ps.gz %X A massive data set is considered as a set of experimentally acquired values of a number of variables each of which is associated with the respective node of an undirected adjacency graph that presets the fixed structure of the data set. The class of data analysis problems under consideration is outlined by the assumption that the ultimate aim of processing can be represented as a transformation of the original data array into a secondary array of the same structure but with node variables of, generally speaking, different nature, i.e. different ranges. Such a generalized problem is set as the formal problem of optimization (minimization or maximization) of a real-valued objective function of all the node variables. The objective function is assumed to consist of additive constituents of one or two arguments, respectively, node and edge functions. The former of them carry the data-dependent information on the sought-for values of the secondary variables, whereas the latter ones are meant to express the a priori model constraints. For the case when the graph of the pair-wise adjacency of the data set elements has the form of a tree, an effective global optimization procedure is proposed which is based on a recurrent decomposition of the initial optimization problem over all the node variables into a succession of partial problems each of which consists in optimization of an intervening function of only one variable like Bellman functions in the classical dynamic programming. Two kinds of numerical realization of the basic optimization procedure are considered on the basis of parametric representation of the Bellman functions, respectively, for discretely defined and quadratic node and edge functions. The proposed theoretical approach to the analysis of massive data sets is illustrated with its applications to the problems of segmentation, smoothing, fine texture analysis and matching of visual images and geophysical explorative data, as well as to the problem of multi-alignment of long molecular sequences. %A Awerbuch, Baruch %A Du, Yi %A Khan, Bilal %A Shavitt, Yuval %T Routing Through Networks with Hierarchical Topology Aggregation %D March 5, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-16 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-16.ps.gz %X In the future, global networks will consist of a hierarchy of subnetworks called domains. For reasons of both scalability and security, domains will not reveal details of their internal structure to outside nodes. Instead, these domains will advertise only a summary, or aggregated view, of their internal structure, e.g., as proposed by the ATM PNNI standard.

This work compares, by simulation, the performance of several different aggregation schemes in terms of network throughput (the fraction of attempted connections that are realized), and network control load (the average number of crankbacks per realized connection.)

Our main results are: Minimum spanning tree is a good aggregation scheme; Exponential link cost functions perform better than min-hop routing; Our suggested logarithmic update scheme that determine when re-aggregation should be computed can significantly reduce the computational overhead due to re-aggregation with a negligable decrease in performance. %A Feder, Tomas %A Shende, Sunil M. %T Online Channel Allocation in FDMA Networks with Reuse Constraints %D March 16, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-17 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-17.ps.gz %X The topology of an FDMA network is modeled by a subdivision of a planar region into hexagonal cells; this defines a graph where every node has at most six neighbors. For channel allocation, every node has a weight that indicates the number of channels that must be assigned to it; the reuse distance defines the minimum distance between nodes that can use the same channel without radio interference. It is known that with reuse distance 2, the number of channels needed and their allocation can be approximated within a factor of $4/3$ both offline and online. We describe an online algorithm for the case of reuse distance 3 that achieves an approximation factor of $7/3$. %A Ibaraki, Toshihide %A Kogan, Alexander %A Makino, Kazuhisa %T Functional Dependencies in Horn Theories %D March 12, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-18 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-18.ps.gz %X This paper studies functional dependencies in Horn theories, both when the theory is represented by its clausal form and when it is defined as the Horn envelope of a set of models. We provide polynomial algorithms for the recognition of whether a given functional dependency holds in a given Horn theory, as well as polynomial algorithms for the generation of some representative sets of functional dependencies that hold in a given Horn theory. We show that some functional dependencies inference problems are computationally difficult. We also study the structure of functional dependencies that hold in a Horn theory, show that every such functional dependency is in fact a single positive term Boolean function, and prove that for any Horn theory the set of its minimal functional dependencies is quasi-acyclic. Finally, we consider the problem of condensing a Horn theory, prove that any Horn theory has a unique condensation, and develop an efficient polynomial algorithm for condensing Horn theories. %A Abrego, Bernardo M. %A Fernandez-Merchant, Silvia %T On the Number of Equilateral Triangles in Euclidean Space I %D April 1, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-19 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-19.ps.gz %X The following problem was posed by Erd\H{o}s and Purdy: ``What is the maximum number of equilateral triangles determined by a set of $n$ points in ${\Bbb R}^{d}$?'' New bounds for this problem are obtained for dimensions 2, 4 and 5. In addition it is shown that for $d=2$ the maximum is attained by subsets of the regular triangle lattice. %A Saniee, Iraj %A Bienstock, Daniel %T ATM Network Design: Traffic Models and Optimization-Based Heuristics %D April 3, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-20 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-20.ps.gz %X We consider the design and capacity expansion of ATM networks as an optimization problem in which flows representing end-to-end variable bit-rate services of different classes are to be multiplexed and routed over ATM trunks and switches so as to minimize the costs of additional switches and transport pipes while meeting service quality and survivability constraints. After discussing the underlying fractional Brownian motion model for aggregate flows, a non-linear multicommodity optimization problem is formulated and heuristics for its approximate solutions are described. Finally, computational results are produced that demonstrate realistic size problems can be solved with the proposed method to shed light on key economic characteristics of ATM traffic, such as safe levels of statistical multiplexing, as well as robust and efficient design alternatives. %A Abbasi, Sarmad %T How tight is the Bollobas-Komlos Conjecture? %D May 6, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-21 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-21.ps.gz %X

The bipartite case of the Bollob\'as and Koml\'os conjecture states that for every $\Delta_0, \gamma >0$ there is an $\alpha = \alpha(\Delta_0, \gamma) >0$ such that the following statement holds:

If $G$ is any graph with minimum degree at least

$${ n \over 2} + \gamma n,$$

then $G$ contains as subgraphs all $n$ vertex bipartite graphs, $H,$ satisfying

$$ \Delta(H) \leq \Delta_0 \mbox{ and } b(H) \leq \alpha n.$$

Here $b(H),$ the bandwidth of $H$, is the smallest $b$ such that the vertices of $H$ can be ordered as $v_1, \ldots, v_n$ such that $ v_i \sim_H v_j$ implies $|i-j| \leq b$.

This conjecture has been proved in [1]. In this note we show that this conjecture is tight in the sense that as $\gamma \rightarrow 0$ then $\alpha \rightarrow 0$. More precisely, we show that for any $\gamma \leq { 1 \over 100}$ there is a $\Delta_0$ such that that $\alpha(\Delta_0, \gamma) \leq 4 \gamma $. %A Toth, Geza %A Valtr, Pavel %T Geometric Graphs with Few Disjoint Edges %D May 7, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-22 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-22.ps.gz %X

A geometric graph is a graph drawn in the plane so that the vertices are represented by points in general position, the edges are represented by straight line segments connecting the corresponding points.

Improving a result of Pach and T\"or\H ocsik, we show that a geometric graph on $n$ vertices with no $k+1$ pairwise disjoint edges has at most $k^3(n+1)$ edges. On the other hand, we construct geometric graphs with $n$ vertices and approximately ${3\over 2}(k-1)n$ edges, containing no $k+1$ pairwise disjoint edges.

We also improve both the lower and upper bounds of Goddard, Katchalski and Kleitman on the maximum number of edges in a geometric graph with no four pairwise disjoint edges. %A Allender, Eric %A Loui, Michael C. %A Regan, Kenneth W. %T Complexity Classes %D May 11, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-23 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-23.ps.gz %X This material was written for Chapter 27 of the CRC Handbook of Algorithms and Theory of Computation, edited by Mikhail Atallah. %A Allender, Eric %A Loui, Michael C. %A Regan, Kenneth W. %T Reducibility and Completeness %D May 11, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-24 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-24.ps.gz %X This material was written for Chapter 28 of the CRC Handbook of Algorithms and Theory of Computation, edited by Mikhail Atallah. %A Allender, Eric %A Loui, Michael C. %A Regan, Kenneth W. %T Other Complexity Classes and Measures %D May 11, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-25 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-25.ps.gz %X This material was written for Chapter 29 of the CRC Handbook of Algorithms and Theory of Computation, edited by Mikhail Atallah. %A Pach, Janos %A Toth, Geza %T Erdos-Szekeres-Type Theorems for Segments and Non-crossing Convex Sets %D May 11, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-26 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-26.ps.gz %X A family $\cal F$ of convex sets is said to be in convex position, if none of its members is contained in the convex hull of the others. It is proved that there is a function $N(n)$ with the following property. If $\cal F$ is a family of at least $N(n)$ plane convex sets with non-empty interiors, such that any two members of $\cal F$ have at most two boundary points in common and any three are in convex position, then $\cal F$ has $n$ members in convex position. This result generalizes a theorem of T. Bisztriczky and G. Fejes Tóth \cite{BF1}. The statement does not remain true, if two members of $\cal F$ may share four boundary points. This follows from the fact that there exist infinitely many straight-line segments such that any three are in convex position, but no four are. However, there is a function $M(n)$ such that every family of at least $M(n)$ segments, any four of which are in convex position, has $n$ members in convex position. %A Toth, Geza %T Finding Convex Sets in Convex Position %D May 22, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-27 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-27.ps.gz %X Let ${\cal F}$ denote a family of pairwise disjoint convex sets in the plane. ${\cal F}$ is said to be in {\em convex position}, if none of its members is contained in the convex hull of the union of the others. For any fixed $k\geq 5$, we give a linear upper bound on $P_k(n)$, the maximum size of a family ${\cal F}$ with the property that any $k$ members of ${\cal F}$ are in convex position, but no $n$ are. %A Galitsky, Boris %T A Formal Scenario and Metalanguage Support Means to Reason about It %D June 3, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-28 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-28.ps.gz %X

We build the reasoning tool of metalanguage support (MS) with the embedded mechanism of the invention of predicates and metapredicates for the comprehension and synthesis tasks. This tool, based on metalanguage representation with weakened soundness, gains the inference flexibility to represent the formal scenarios (for example, a limited class of "logical" anecdotes, derived from NL). We introduce the concept of formal scenario as an alternative to the traditional axiomatic method (logical program) for the practical applications and develop specific MS means to perform the reasoning within a formal scenario. The anecdote scenario is an appealing object of study in the logical programming because it reflects the top level of human intellectual activity on one hand and is rather compact on the other.

We present such applications as scenario comprehension and generation, genetic algorithm of MS formula modifications, NL aspects of scenarios and modeling of the psychological disorder with corrupted pretending and believing concepts (autism). Such MS capabilities for scenario representation as reasoning about action, change and belief, temporal and spatial reasoning, are illustrated.

MS is based on the rules of metalanguage transfer (inconsistency shift, variability shift and assumption enforcement), which connect the object level with the metalevel and introduce a number of ways to construct the scenario explanation predicates. %A Pach, Janos %A Toth, Geza %T Which Crossing Number Is It Anyway? %D June 11, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-29 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-29.ps.gz %X A drawing of a graph $G$ is a mapping which assigns to each vertex a point of the plane and to each edge a simple continuous arc connecting the corresponding two points. The crossing number of $G$ is the minimum number of crossing points in any drawing of $G$. We define two new parameters, as follows. The pairwise crossing number (resp. the odd-crossing number) of $G$ is the minimum number of pairs of edges that cross (resp. cross an odd number of times) over all drawings of $G$. We prove that the determination of each of these parameters is an NP-complete problem. We also prove that the largest of these numbers (the crossing number) cannot exceed twice the square of the smallest (the odd-crossing number). Our proof is based on the following generalization of an old result of Hanani, which is of independent interest. Let $G$ be a graph and let $E_0$ be a subset of its edges such that there is a drawing of $G$, in which every edge belonging $E_0$ crosses any other edge an even number of times. Then $G$ can be redrawn so that the elements of $E_0$ are not involved in any crossing. %A Korupolu, Madhukar R. %A Plaxton, C. Greg %A Rajaraman, Rajmohan %T Analysis of a Local Search Heuristic for Facility Location Problems %D June 24, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-30 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-30.ps.gz %X In this paper, we study approximation algorithms for several NP-hard facility location problems. We prove that a simple local search heuristic yields polynomial-time constant-factor approximation bounds for the metric versions of the uncapacitated k-median problem and the uncapacitated facility location problem. (For the k-median problem, our algorithms require a constant-factor blowup in the parameter k.) This local search heuristic was first proposed several decades ago, and has been shown to exhibit good practical performance in empirical studies. We also extend the above results to obtain constant-factor approximation bounds for the metric versions of capacitated k-median and facility location problems. %A Krivelevich, Michael %A Sudakov, Benny %T Approximate Coloring of Uniform Hypergraphs %D July 9, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-31 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-31.ps.gz %X We consider an algorithmic problem of coloring r-uniform hypergraphs. The problem of finding the exact value of the chromatic number of a hypergraph is known to be NP$hard, so we discuss approximate solutions to it. Using a simple construction and known results on hardness of graph coloring, we show that for any r\>= 3 it is impossible to approximate in polynomial time the chromatic number of r-uniform hypergraphs on n vertices within a factor n^{1-epsilon} for any epsilon>0, unless NP is a subset of ZPP. On the positive side, we present an approximation algorithm for coloring r-uniform hypergraphs on n vertices, whose performance ratio is O(n(loglog n)^2/(\log n)^2). We also describe an algorithm for coloring 3-uniform 2-colorable hypergraphs on n vertices in O(n^{9/41}) colors, thus improving previous results of Chen and Frieze and of Kelsen, Mahajan and Ramesh. %A Alon, Noga %A Krivelevich, Michael %A Sudakov, Benny %T Coloring Graphs with Sparse Neighborhoods %D July 9, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-32 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-32.ps.gz %X It is shown that the chromatic number of any graph with maximum degree d in which the number of edges in the induced subgraph on the set of all neighbors of any vertex does not exceed d^2/f is at most O( d/ \log f). This is tight (up to a constant factor) for all admissible values of d and f. %A Hegyvari, Norbert %T Thin Complete Subsequence %D July 13, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-33 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-33.ps.gz %X

$A$ is said to be {\em complete} if every sufficiently large integer belongs to the sumset of $A$. $A'$ is {\em thin comlete subsequence} of $A$ if $A'$ is complete and $A'(x)=(1+o(1))\log_2x$.

It is proved that $\lim_{n\to \infty}a_{n+1}/a_n=1$ implies the existence of thin complete subsequence. %A Hegyvari, Norbert %T On the Dimension of the Hilbert-Cubes %D July 13, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-34 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-34.ps.gz %X Let $A$ be a sequence of positive integers with positive density. Then $A\cap\{1, 2, \ldots , n\}$ contains a Hilbert (or combinatorial) cube of dimension $c\log\log n$. We prove that this bound can not be replaced by $c'\sqrt{\log n\log\log n}$. %A Abbasi, Sarmad %T Do Answers Help in Posing Questions? %D July 14, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-35 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-35.ps.gz %X Let $T_n$ denote a complete binary tree of depth $n$. Each internal node, $v$, of $T_n$ has two children denoted by $\lf(v)$ and $\rt(v)$. Consider the following game between two Players, Paul and Carole. For each internal node, $v$, Carole chooses $X(v) \in \{ \lf(v) , \rt(v) \}$. This naturally defines a path from the root, $\lambda$, of $T_n$ to one of its leaves as follows: $$\lambda, X(\lambda), X^2(\lambda ), \ldots, X^n(\lambda).$$ Paul has to find this path by asking questions of the following form:

\smallskip \centerline{$Q_v$:``Is $X(v) = \lf(v)$?''} \smallskip

\noindent The game proceeds in $r$ rounds. In every round Paul can $k$ questions. Carole supplies the answers to these $k$ questions in parallel. We give necessary and sufficient conditions for Paul to win this game. %A Liberatore, Vincenzo %T Broadcast Disk Paging with a Small Cache %D July 16, 1998 %Z Sat, 19 Sep 1998 20:00:00 GMT %I DIMACS %R 98-36 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-36.ps.gz %X We consider the broadcast disk paging problem when the cache size is 2 and n pages are transmitted. We show an algorithm that is (n - 2 / (n - 2))-competitive and prove that no better competitive ratio is possible. %A Kalantari, Bahman %T Scaling Dualities and Self-Concordant Homogeneous Programming in Finite Dimensional Spaces %D July 20, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-37 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-37.ps.gz %X In this paper first we prove four fundamental theorems of the alternative, called scaling dualities, characterizing exact and approximate solvability of four significant conic problems in finite dimensional spaces, defined as: homogeneous programming (HP), scaling problem (SP), homogeneous scaling problem (HSP), and algebraic scaling problem (ASP), the problem of testing the solvability of the scaling equation (SE), a fundamental equation inherited from properties of homogeneity. These four problems together with the scaling dualities offer a new point of view into the theory and practice of convex and nonconvex programming. Nontrivial special cases over the nonnegative orthant include: testing if the convex-hull of a set of points contains the origin (equivalently, testing the solvability of Karmarkar's canonical LP), computing the minimum of the arithmetic-geometric mean ratio over a subspace, testing the solvability of the diagonal matrix scaling equation (DADe=e), as well as NP-complete problems. The scaling dualities closely relate these seemingly unrelated problems. Via known conic LP dualities, convex programs can be formulated as HP. Scaling dualities go one step further, allowing us to view HP as a problem dual to the corresponding SP, HSP, or ASP. This duality is in the sense that HP is solvable if and only if the other three are not. Our scaling dualities give nontrivial generalization of the arithmetic-geometric mean, trace-determinant, and Hadamard inequalities; matrix scaling theorems; and the classic duality of Gordan. We describe potential-reduction and path-following algorithms for these four problems, resulting in novel and conceptually simple polynomial-time algorithms for linear, quadratic, semidefinite, and self-concordant programming. Furthermore, the algorithms are more powerful than their existing counterparts, since they also establish the polynomial-time solvability of the corresponding SP, HSP, as well as many cases of ASP. The scaling problems either have not been addressed in the literature, or have been treated in very special cases. The algorithms are based on the scaling dualities, significant bounds obtained in this paper, properties of homogeneity, as well as Nesterov and Nemirovskii's machinery of self-concordance. In particular, our results extend the polynomial-time solvability of matrix scaling equation (even in the presence of a subspace) to general cases of SE over the nonnegative cone, or the semidefinite cone, or the second-order cone. %A Kalantari, Bahman %T On the Arithmetic-Geometric Mean Inequality and Its Relationship to Linear Programming, Matrix Scaling, and Gordan's Theorem %D July 20, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-38 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-38.ps.gz %X It is a classical inequality that the minimum of the ratio of the (weighted) arithmetic mean to the geometric mean of a set of positive variables is equal to one, and is attained at the center of the positivity cone. While there are numerous proofs of this fundamental homogeneous inequality, in the presence of an arbitrary subspace, and/or the replacement of the arithmetic mean with an arbitrary linear form, the new minimization is a nontrivial problem. We prove a generalization of this inequality, also relating it to linear programming, to the diagonal matrix scaling problem, as well as to Gordan's theorem. Linear programming is equivalent to the search for a nontrivial zero of a linear or positive semidefinite quadratic form over the nonnegative points of a given subspace. The goal of this paper is to present these intricate, surprising, and significant relationships, called {\it scaling dualities}, and via an elementary proof. Also, to introduce two conceptually simple polynomial-time algorithms that are based on the scaling dualities, significant bounds, as well as Nesterov and Nemirovskii's machinery of self-concordance. The algorithms are simultaneously applicable to linear programming, to the computation of a separating hyperplane, to the diagonal matrix scaling problem, and to the minimization of the arithmetic-geometric mean ratio over the positive points of an arbitrary subspace. The scaling dualities, the bounds, and the algorithms are special cases of a much more general theory on convex programming, developed by the author. For instance, via the scaling dualities semidefinite programming is a problem dual to a generalization of the classical trace-determinant ratio minimization over the positive definite points of a given subspace of the Hilbert space of symmetric matrices. %A Alexander K. Kelmans %T Crossing Properties of Graph Reliability Functions %D August 10, 1998 %Z Thu, 19 Nov 1998 20:00:00 GMT %I DIMACS %R 98-39 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-39.ps.gz %X We consider undirected graphs, and assume that each edge of $G$ exists with probability $p \in (0,1)$. The all--terminal reliability function of such a random graph $G$ is the probability that the spanning subgraph formed by the existing edges is connected. A two--graph is a graph with two distinguished vertices called terminals. The two--terminal reliability function of a two--graph $G$ is the probability that the subgraph of $G$ induced by the existing edges contains a path connecting the terminals. Till recently no examples of pairs of graphs have been known whose all--terminal or two--terminal reliabilities cross more than twice and only one example of exactly two crossings. In [8] we proved that for every integer $N$ there exist pairs of graphs (two--graphs) whose all--terminal (respectively, two--terminal) reliabilities cross more than $N$ times. In this paper we give simple constructions that provide, for every set $\{(n_1,m_1), \ldots (n_k,m_k)\}$ of ordered pairs of integers (where all $m_i$ are distinct), a pair of graphs (two--graphs) of the same size whose all--terminal (respectively, two--terminal) reliability functions have exactly $n_1 + \ldots + n_k$ crossings and exactly $n_i$ crossings of multiplicity $m_i$ for every $i = 1, \ldots , k$. %A Muthukrishnan, S. %A Rajaraman, R. %T An Adversarial Model for Distributed Dynamic Load Balancing %D August 10, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-40 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-40.ps.gz %X

We study the problem of balancing the load on processors of an arbitrary network. If jobs arrive or depart during the process of load balancing, we have the dynamic load balancing problem; otherwise, we have the static load balancing problem. While static load balancing on arbitrary and special networks has been well studied, very little is known about dynamic load balancing. The difficulty lies in modeling the arrivals and departures of jobs in a clean manner.

In this paper, we initiate the study of dynamic load balancing by modeling job traffic using an adversary. Our main result is that a simple, local control distributed load balancing algorithm maintains the load of the network within a stable level against this powerful adversary. Our results hold for different models of traffic patterns and processor communication. %A Barg, Alexander %A Guritman, Sugi %A Simonis, Juriaan %T Strengthening the Varshamov-Gilbert Bound %D August 13, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-41 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-41.ps.gz %X The paper discusses some ways to strengthen (nonasymptotically) the Gilbert-Varshamov bound for linear codes. The unifying idea is to study a certain graph constructed on vectors of low weight in the cosets of the code, which we call the Varshamov graph. Various simple estimates of the number of its connected components account for better lower bounds on the minimum distance of codes, some of them known in the literature. %A Yu, Yang %T Note on the Permanent Rank of a Matrix %D September 1, 1998 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 98-42 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-42.ps.gz %X Define the perrank of a matrix $A$ to be the size of a largest square submatrix of $A$ with nonzero permanent. Motivated in part by the Alon-Jaeger-Tarsi Conjecture \cite{at}, we prove several results on perranks. %A Ahmed Belal %A Magdy A.Ahmed %A Shymaa M.Arafat %D September 13, 1998 %Z Wed, 25 Nov 1998 20:00:00 GMT %I DIMACS %R 98-43 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-43.ps.gz %X

Two-dimensional alphabetic trees have many applications in a wide variety of diverse fields. Despite the existense of a relatively fast algorithm that finds an approximate 2-dimensional optimal alphabetic tree(OAT), a dynamic programming approach must still be used to determine the exact solution.To apply dynamic programming, the (OAT) can be found by examining all the nodes in the 2-d array of weights as possible roots for the optimal tree. In this paper we introduce the concept of goodness for each cut to limit the search for an optimal solution.The measure of goodness is a value we call the expense of the cut, only cuts with expense less than a given limit L are considered good cuts. At every level of the tree only the good cuts are tested as possible candidates for an optimal solution.

Key Words : alphabetic tree, optimal tree, dynamic programming, two dimensional alphabetic trees, branch and bound.

%A Csaba, Bela %A Lodha, Sachin %T List Update Problem %D September 17, 1998 %Z Sat, 19 Sep 1998 20:00:00 GMT %I DIMACS %R 98-44 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-44.ps.gz %X We present an optimal on-line algorithm for the List Update Problem when the request sequence has some particular structure. %A Carol J. Feltz %A Gerald A. Goldin %T Partition-Based Goodness-of-Fit Tests on the Line and the Circle %D October 1, 1998 %Z Thu, 19 Nov 1998 20:00:00 GMT %I DIMACS %R 98-45 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-45.ps.gz %X We propose a way to construct consistent generalizations of the Cram\'er-von Mises test on the line, and the Watson $U_n^{\,2}$ test on the circle, based on classes of partitions invariant under various group actions. The framework developed extends our earlier work generalizing the Kolmogorov-Smirnov and Kuiper goodness-of-fit tests, and provides a conceptually unifying description. Many goodness-of-fit tests for uniformity on the circle incorporate rotation invariance. Our construction does not require that the distribution for the null hypothesis be uniform, and permits tests invariant under general coordinate transformations. Some distribution-free tests are presented as examples, and their properties explored through numerical simulations.

Key words and phrases: Distribution-free tests; Kolmogorov-Smirnov test; Kuiper's test; Cram\'er-von Mises test; Watson $U_n^{\,2}$ test.

%A Farhad Shahrokhi %A Weiping Shi %T On Crossing Sets, Disjoint Sets and the Pagenumber %D October 5, 1998 %Z Thu, 19 Nov 1998 20:00:00 GMT %I DIMACS %R 98-46 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-46.ps.gz %X Let $G=(V,E)$ be a $t$-partite graph with $n$ vertices and $m$ edges, where the partite sets are given. We present an $O(n^2m^{1.5})$ time algorithm to construct drawings of $G$ in the plane so that the size of the largest set of pairwise crossing edges, and at the same time, the size of the largest set of disjoint (pairwise non-crossing) edges are $O(\sqrt{t\cdot m})$. As an application we embed $G$ in a book of $O(\sqrt{t\cdot m})$ pages, in $O(n^2m^{1.5})$ time, resolving an open question for the pagenumber problem. A similar result is obtained for the dual of the pagenumber or the queuenumber. Our algorithms are obtained by derandomizing a probabilistic proof. %A Oliver Attie %T Quasi-isometry Classification of Coarse Hadamard Manifolds %D October 12, 1998 %Z Thu, 19 Nov 1998 20:00:00 GMT %I DIMACS %R 98-47 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-47.ps.gz %X

Quasi-conformal mappings were first introduction by L. Ahlfors in 1935, in connection with open Riemann surfaces and value distribution theory, and then studied by O. Teichm\"uller in 1938. In 1956 A. Beurling and Ahlfors proved an extension theorem which states that a quasi-symmetric map $\phi:{\bold R\/} \to {\bold R\/}$ can be extended to a quasiconformal map of the upper half plane. In 1964 Ahlfors had proven a similar theorem for quasi-symmetric mappings of ${\bold R\/}^2$. Then in 1979 P. Tukia and J. V\"ais\"al\"a a proved quasiconformal extension to dimensions $\geq 5$. The case of extension from 3 to 4 dimensions is still unknown.

In this paper we prove three main quasi-conformal extension results. First we prove the Tukia-V\"ais\"al\"a theorem, which states that a quasiconformal map of upper half space ${\bold R_+^{n+1} \to {\bold R\/}_+^{n+1}$ provided $n \geq 5$. The second result is a similar extension theorem for the strongly uniform domains introduced by Heinonen and Yang 1993. Finally, we solve a problem posed Pansu in 1989 regarding the existence of a quasiconformal extension theorem for complex hyperbolic spaces. We can in fact prove this result for manifolds of pinched negative curvature.

%A Oliver Attie %A Jonathan Block %T Poincaré Duality for Lp Cohomology and Characteristic Classes %D October 30, 1998 %Z Thu, 19 Nov 1998 20:00:00 GMT %I DIMACS %R 98-48 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-48.ps.gz %X We prove Poincar\'e Duality for $L^p$ cohomology, $1 \leq p \leq \infty$ We study the pairings between $L^p$ and $L^\infty$ and construct characteristic classes. %A Fred S. Roberts %A Li Sheng %T Phylogeny Numbers for Graphs with Two Triangles %D October 31, 1998 %Z Thu, 19 Nov 1998 20:00:00 GMT %I DIMACS %R 98-49 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-49.ps.gz %X Motivated by problems of phylogenetic tree reconstruction, we introduce notions of phylogeny graph and phylogeny number. These notions are analogous to and can be considered as natural generalizations of notions of competition graph and competition number that arise from problems of ecology. Given an acyclic digraph $D=(V,A)$, define its {\em phylogeny graph} $G=P(D)$ by taking the same vertex set as $D$ and, for $x\neq y$, letting $xy\in E(G)$ if and only if $(x,y)\in A$ or $(y,x)\in A$ or $(x,a), (y,a) \in A$ for some vertex $a\in V$. Given a graph $G=(V,E)$, we shall call the acyclic digraph $D$ a {\em phylogeny digraph} for $G$ if $G$ is an induced subgraph of $P(D)$ and $D$ has no arcs from vertices outside of $G$ to to vertices in $G$. The {\em phylogeny number} $p(G)$ is defined to be the smallest $r$ such that $G$ has a phylogeny digraph $D$ with $|V(D)|-|V(G)|=r$. In this paper, we obtain results about phylogeny number for graphs with exactly two triangles analogous to those for competition number. %A Fred S. Roberts %A Li Sheng %T Extremal Phylogeny Numbers %D October 31, 1998 %Z Thu, 19 Nov 1998 20:00:00 GMT %I DIMACS %R 98-50 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-50.ps.gz %X Given an acyclic digraph $D=(V,A)$, define its {\em phylogeny graph} $G=P(D)$ by taking the same vertex set as $D$ and, for $x\neq y$ in $V$, letting $xy\in E(G)$ if and only if $(x,y)\in A$ or $(y,x)\in A$ or $(x,a), (y,a) \in A$ for some vertex $a\in V$. Given a graph $G=(V,E)$, we shall call the acyclic digraph $D$ a {\em phylogeny digraph} for $G$ if $G$ is an induced subgraph of $P(D)$ and $D$ has no arcs from vertices outside of $G$ to $G$. The {\em phylogeny number} $p(G)$ is defined to be the smallest $r$ such that $G$ has a phylogeny digraph $D$ with $|V(D)|-|V(G)|=r$. In this paper, we apply the famous theorem of Tur\'an to show that for graph $G$ with $n$ vertices, $p(G)\le \lfloor\frac{n^2}{4}\rfloor -n+1$ and that $p(G)$ achieves this upper bound if and only if $n\le 3$ or $G=K(\lfloor\frac{n}{2}\rfloor, \lceil\frac{n}{2}\rceil)$. %A Durand, Dannie %A Eric Bendix %A Kristin Ardlie %A Warren Ewens %A Lee Silver %T Genetic Drift in Populations of Ultraselfish Gene Complexes %D November 13, 1998 %Z Fri, 26 Feb 1999 18:00:00 GMT %I DIMACS %R 98-51 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-51.ps.gz %X

Abstract: We use stochastic population models to study the evolution of Ultraselfish Gene Complexes (USGC's). USGC's are chromosomal regions characterized by segregation distortion: a heterozygote bearing the USGC passes it to more than 50 of offspring. USGC-bearing homozygotes are sterile. USGC's promote themselves at the expense of other genes in the same genome. They have been observed in animal, plant and fungal species and may lie, undetected, in many others. While the molecular drive mechanisms differ, USGC's exhibit similar genetic features, suggesting that the fundamental evolutionary mechanisms that allow their emergence may be shared.

We present Markov models and Monte Carlo simulations of genetic drift in populations of USGC's. Genetic drift, the stochastic behavior of allele frequencies in small populations, is a fundamental force in the process of evolution, yet the role of genetic drift in the evolution of USGC's is not well understood. Our analysis shows how genetic drift causes USGC's to evolve different characteristics in species typified by small and large populations, respectively. We apply our results to two well studied USGC's: the $t$-haplotype in Mus musculus and Segregation Distorter in Drosophila melanogaster.

%A Shahrokhi, Farhad %A Ondrej Sykora %A Laszlo A. Szekely %A Imrich Vrto %T A New Lower Bound for the Bipartite Crossing Number with Applications %D November 19, 1998 %Z Thu, 19 Nov 1998 20:00:00 GMT %I DIMACS %R 98-52 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-52.ps.gz %X Let $G$ be a connected bipartite graph.% on $n$-vertices. We give a short proof, using a variation of Menger's Theorem, for a new lower bound which relates the bipartite crossing number of $G$, denoted by $bcr(G)$, to the edge connectivity properties of $G$. The general lower bound implies a weaker version of a very recent result, establishing a bisection based lower bound on $bcr(G)$ which has algorithmic consequences. Moreover, we show further applications of our general method to estimate $bcr(G)$ for ``well structured'' families of graphs, for which tight isoperimetric inequalities are available. For hypercubes and 2-dimensional meshes, the upper bounds (asymptotically) are within multiplicative factors of $4$ and $2$, from the lower bounds, respectively. The general lower bound also implies a lower bound involving eigenvalues of $G$. %A Ashikhmin, A. %A Barg, A. %A Litsyn, S. %T New Upper Bounds on Generalized Weights %D November 23, 1998 %Z Wed, 21 Jan 1999 18:00:00 GMT %I DIMACS %R 98-53 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-53.ps.gz %X We derive new asymptotic upper bounds on the generalized weights of a binary linear code of a given size. We also prove some asymptotic results on the distance distribution of binary codes. %A Dolev, Shlomi %A Ostrovsky, Rafail %T Xor-Trees for Efficient Anonymous Multicast and Reception %D December 23, 1998 %Z Wed, 21 Jan 1999 18:00:00 GMT %I DIMACS %R 98-54 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-54.ps.gz %X In this work we examine the problem of efficient anonymous broadcast and reception in general communication networks. We show an algorithm which achieves anonymous communication with O(1) amortized communication complexity on each link and low computational complexity. In contrast, all previous solutions require polynomial (in the size of the network and security parameter) amortized communication complexity. %A DIMACS %T Scientific Achievements at DIMACS: Highlights of the Second Four Years %D December 24, 1998 %Z Fri, 26 Feb 1999 18:00:00 GMT %I DIMACS %R 98-55 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-55.ps.gz %X This report highlights some of the many notable research accomplishments of center members, postdoctoral fellows, graduate students, and visitors whose work was impacted by DIMACS' programs. This report covers the years 1993-1997. %A Chari, Suresh %A Rohatgi, Pankaj %A Srinivasan, Aravind %T Improved Algorithms via Approximations of Probability Distributions %D January 14, 1997 %Z Fri, 17 Jan 1997 13:03:33 GMT %I DIMACS %R 97-01 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-01.ps.gz %X We present two techniques for approximating probability distributions. The first is a simple method for constructing the small-bias probability spaces introduced by Naor and Naor. We show how to efficiently combine this construction with the method of conditional probabilities to yield improved NC algorithms for many problems such as set discrepancy, finding large cuts in graphs, finding large acyclic subgraphs etc. The second is a construction of small probability spaces approximating general independent distributions, which is of smaller size than the constructions of Even, Goldreich, Luby, Nisan and Velickovic. Such approximations are useful, e.g., for the derandomization of certain randomized algorithms.

In addition to other support, Aravind Srinivasan's research was supported in part by NSF grant NSF-STC91-19999 to DIMACS and by support to DIMACS from the New Jersey Commission on Science and Technology. %A Carpenter, Tamra %A Cosares, Steven %A Saniee, Iraj %T Demand Routing and Slotting on Ring Networks %D January 28, 1997 %Z Thu, 13 Feb 1997 21:46:48 GMT %I DIMACS %R 97-02 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-02.ps.gz %X We describe an important class of problems that arise in the economic design of "survivable" networks. Such networks are capable of accommodating all of the traffic between pairs of locations, even if some arbitrary link or node in the network is rendered unusable. Cycles play an important role in the design of survivable networks because they represent two-connected subnetworks of minimal size. To cost-effectively utilize cycles, we must determine the minimum capacity required for the links in the cycle, subject to constraints on how traffic must be routed and how capacity must be utilized. Depending upon the situation being modeled, different versions of the problem arise. The least restrictive versions are solvable in polynomial time, while the more restrictive (and more realistic) versions are NP-hard. This paper focuses on variants of the problem in which time-slot assignment constraints are enforced to model the operation of the equipment placed at the nodes of a SONET ring. We present several simple heuristic methods for addressing the problem, and we show that they are 2-approximation algorithms. %A Todorcevic, Stevo %A Vaananen, Jouko %T Trees and Ehrenfeucht-Fraisse games %D February 5, 1997 %Z Wed, 5 Feb 1997 18:47:25 GMT %I DIMACS %R 97-03 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-03.ps.gz %X We study trees T of height at most omega-1 with no uncountable branches, and their applications in the study of pairs (A,B) of non-isomorphic structures over a fixed vocabulary. There is a natural quasi-ordering of such trees in terms of the existence of a strictly increasing mapping from one tree to another. We investigate in depth the structure of this quasi-ordering and relate its properties to properties of pairs (A,B) of structures. Many new constructions of pairs of highly equivalent non-isomorphic structures are given. %A Fang, Weiwu %T On a Global Optimization Problem in the Study of Information Discrepancy %D February 5, 1997 %Z Wed, 5 Feb 1997 18:50:20 GMT %I DIMACS %R 97-04 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-04.ps.gz %X A nonlinear function has been introduced for indexing the disagreement degree of a group of judgment matrices (in FW, 1994). It has many good properties and may be applied in decision making and information process. In this paper, we will discuss a global optimization problem concerned with the global maximum of this function which is constrained on some sets of matrices. Because the size of matrix groups in the problem is arbitrary and the number of local maximum solutions increases exponentially, numerical methods are not suitable and formalized results are desired for the problem. By an approach somewhat similar to the branch and bounded method, we have obtained some formulae on global maximums, a sufficient and necessary condition of the function's taking the maximums, and its some maximum solution sets. %A Lisitsa, Alexei %A Sazonov, Vladimir %T On linear ordering finitely-branching graphs and non-well-founded sets %D February 6, 1997 %Z Tue, 25 Feb 1997 19:16:50 GMT %I DIMACS %R 97-05 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-05.ps.gz %X Definability of a linear order in finite structures of some given class by logical means is an important issue of finite model theory and descriptive complexity theory. For example, first-order logic extended by least fixed point operator (FO+LFP) describes exactly PTIME-computability over finite linear ordered structures \cite{Imm82,Var82,Imm86}. If the structures considered are not linearly ordered in advance, but some order may be uniformly definable in FO+LFP then the same result holds for this class of structures, as well.

We will show in this paper that this is the case for the class of finite strongly extensional (SE) graphs (i.e. arbitrary graphs considered up to bisimulation equivalence relation). The vertices of such graphs serve as a faithful representation of hereditarily-finite non-well-founded sets HFA (with finite transitive closure). Actually, we define in FO+IFP a linear ordering on arbitrary SE finitely branching graphs which may be infinite and so represent a more general class of hereditarily-finite non-well-founded sets HFA^{\infty} (with infinite transitive closure).

Our interest to these questions arose from our work on characterizing the complexity classes of computable set-theoretic operations by some bounded set-theory (BST) languages \cite{Saz87,Saz93,Saz95,SaLi95, LiSa97}. So, definability in the language $\Delta_{D}$ considered in \cite{Saz95} over HFA-sets was characterised in terms of definablity in FO+LFP over finite graphs of the abovementioned kind.

Now, having definable linear ordering, we answer affirmatively the question in op. cit. on coincidence of $\Delta_{D}$-definability with PTIME-computability over HFA.

We propose two different definitions of linear ordering, one of which is an application of the method of A.Dawar, S.Lindell and S.Weinstein to the case of SE graphs and give a comparison of both approaches in terms of coherence of the orders on different graphs.

Cf. also related papers in ftp://ftp.botik.ru/rented/logic/papers/ http://www.botik.ru/PSI/AIReC/logic/

-------------------

Both authors from Program Systems Institute of Russian Acad. of Sci., Pereslavl-Zalessky, 152140, Russia.

e-mail: sazonov@logic.botik.rulisitsa@logic.botik.ru

phones: +7-08535-98945 and 98942, fax: +7-08535-20566.

Supported by RBRF (project 96-01-01717).

The work on this paper was started when the second author visited Princeton and Rutgers Universities (DIMACS) in 1996. %A Shelah, Saharon %T Erdos and Renyi Conjecture %D February 11, 1997 %Z Tue, 4 Mar 1997 16:06:41 GMT %I DIMACS %R 97-06 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-06.ps.gz %X Affirming a conjecture of P. Erdos and R\'enyi we prove that for any $c_1 > 0$ for some $c_2 > 0$, if a graph $G$ has no $c_1\ \ \log n$ nodes on which the graph is complete or edgeless (i.e. $G$ exemplifies $|G| \nrightarrow (c_1 \text{ log } n)^2_2$) \underbar{then} $G$ has at least $2^{c_2n}$ non-isomorphic (induced) subgraphs. %A Valtr, Pavel %T On geometric graphs with no k pairwise parallel edges %D March 6, 1997 %Z Fri, 15 Mar 1997 00:17:08 GMT %I DIMACS %R 97-07 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-07.ps.gz %X A {\em geometric graph\/} is a graph $G=(V,E)$ drawn in the plane so that the vertex set $V$ consists of points in general position and the edge set $E$ consists of straight line segments between points of $V$. Two edges of a geometric graph are said to be {\em parallel\/}, if they are opposite sides of a convex quadrilateral.

In this paper we show that, for any fixed $k\ge3$, any geometric graph on $n$ vertices with no $k$ pairwise parallel edges contains at most $O(n)$ edges, and any geometric graph on $n$ vertices with no $k$ pairwise crossing edges contains at most $O(n\log n)$ edges. We also prove a conjecture of Kupitz that any geometric graph on $n$ vertices with no pair of parallel edges contains at most $2n-2$ edges. %A Derrida, B. %A Lebowitz, J. L. %A Speer, E. R. %T Shock Profiles for the Partially Asymmetric Simple Exclusion Process %D March 7, 1997 %Z Fri, 7 Mar 1997 19:47:32 GMT %R 97-08 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-08.ps.gz %X The asymmetric simple exclusion process (ASEP) on a one-dimensional lattice is a system of particles which jump at rates $p$ and $1-p$ (here $p>1/2$) to adjacent empty sites on their right and left respectively. The system is described on suitable macroscopic spatial and temporal scales by the inviscid Burgers' equation; the latter has shock solutions with a discontinuous jump from left density $\rho_-$ to right density $\rho_+$, $\rho_-<\rho_+$, which travel with velocity $(2p-1)(1-\rho_+-\rho_-)$. In the microscopic system we may track the shock position by introducing a second class particle, which is attracted to and travels with the shock. In this paper we obtain the time invariant measure for this shock solution in the ASEP, as seen from such a particle. The mean density at lattice site $n$, measured from this particle, approaches $\rho_{\pm}$ at an exponential rate as $n\to\pm\infty$, with a characteristic length which becomes independent of $p$ when $p/(1-p)>\sqrt{\rho_+(1-\rho_-)/\rho_-(1-\rho_+)}$. When $p/(1-p)=\rho_+(1-\rho_-)/\rho_-(1-\rho_+)$ the measure is Bernoulli, with density $\rho_-$ on the left and $\rho_+$ on the right. In the weakly asymmetric limit, $2p-1\to0$, the microscopic width of the shock diverges as $(2p-1)^{-1}$. The stationary measure is then essentially a superposition of Bernoulli measures, corresponding to a convolution of a space-dependent density profile described by the viscous Burgers equation with a well-defined distribution for the location of the second class particle. %A Nielaba, P. %A Lebowitz, J.L. %T Phase Transitions in the Multicomponent Widom--Rowlinson Model and in Hard Cubes on the BCC--Lattice %D March 14, 1997 %Z Fri, 14 Mar 1997 23:48:30 GMT %I DIMACS %R 97-09 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-09.ps.gz %X We use Monte Carlo techniques and analytical methods to study the phase diagram of the $M$--component Widom--Rowlinson model on the bcc--lattice: there are $M$ species all with the same fugacity $z$ and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for $M \geq 3$ there is a ``crystal phase'' for $z$ lying between $z_c(M)$ and $z_d(M)$ while for $z > z_d(M)$ there are $M$ demixed phases each consisting mostly of one species. For $M=2$ there is a direct second order transition from the gas phase to the demixed phase while for $M \geq 3$ the transition at $z_d(M)$ appears to be first order putting it in the Potts model universality class. For $M$ large, Pirogov-Sinai theory gives $z_d(M) \sim M-2+2/(3M^2) + ... $. In the crystal phase the particles preferentially occupy one of the sublattices, independent of species, i.e.\ spatial symmetry but not particle symmetry is broken. For $M \to \infty$ this transition approaches that of the one component hard cube gas with fugacity $y = zM$. We find by direct simulations of such a system a transition at $y_c \simeq 0.71$ which is consistent with the simulation $z_c(M)$ for large $M$. This transition appears to be always of the Ising type. %A Malkhi, Dahlia %A Reiter, Michael %A Wool, Avishai %T Optimal Byzantine Quorum Systems %D March 17, 1997 %Z Wed, 9 Apr 1997 18:02:30 GMT %I DIMACS %R 97-10 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-10.ps.gz %X Replicated services accessed via quorums enable each access to be performed at only a subset (quorum) of the servers, and achieve consistency across accesses by requiring any two quorums to intersect. Recently, b-masking quorum systems, whose intersections contain at least 2b+1 servers, have been proposed to construct replicated services tolerant of b arbitrary (Byzantine) server failures. In this paper we consider a hybrid fault model allowing benign failures in addition to the Byzantine ones. We present four novel constructions for b-masking quorum systems, each of which has optimal load (the probability of access of the busiest server) or optimal availability (probability of some quorum surviving failures). To show optimality we also prove lower bounds on the load and availability of any b-masking quorum system in this model. %A Valtr, Pavel %T On the density of subgraphs in a graph with bounded independence number %D March 18, 1997 %Z Fri, 21 Mar 1997 16:40:05 GMT %I DIMACS %R 97-11 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-11.ps.gz %X Let $\sigma(n,m,k)$ be the largest number $\sigma\in[0,1]$ such that any graph on $n$ vertices with independence number at most $m$ has a subgraph on $k$ vertices with at least $\sigma\cdot{k\choose 2}$ edges. Up to a constant multiplicative factor, we determine $\sigma(n,m,k)$ for all $n,m,k$. For $\log n\le m=k\le n$, our result gives $\sigma(n,m,m)=\Theta({\log(n/m)\over m})$, which was conjectured by Alon. %A Chen, Hui %T Threshold of Broadcast in Random Graphs %D April 2, 1997 %Z Tue, 2 Apr 1997 00:10:03 GMT %R 97-12 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-12.ps.gz %X Broadcasting process is to send a piece of information which resides at one nodein the graph to all the remaining nodes. At each time step, a node knows about the information can send it to one of its neighbors. The broadcast problem is to find the minimum time step needed. The problem is NP hard in general. For a random graph $G_{n,p}$, we are interested in at what value of $p$ there exists a broadcast tree of depth exactly $\lc \log _2n\rc $. Frieze and Molloy \cite{FriMo} show that $p$ is of magnitude $\Theta ( \ln n/n)$. In this paper, we give the exact threshold of theedge probability for the existence of such a tree. %A Karolyi, Gyula %A Pach, Janos %A Toth, Geza %A Valtr, Pavel %T Ramsey-Type Results for Geometric Graphs. II %D April 4, 1997 %Z Mon, 7 Apr 1997 19:57:59 GMT %R 97-13 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-13.ps.gz %X We show that for any 2--coloring of the ${n \choose 2}$ segments determined by $n$ points in the plane, one of the color classes contains non-crossing cycles of lengths $3,4,\ldots,\lfloor\sqrt{n/2}\rfloor$. This result is tight up to a multiplicative constant. Under the same assumptions, we also prove that there is a non-crossing path of length $\Omega(n^{2/3})$, all of whose edges are of the same color. In the special case when the $n$ points are in convex position, we find longer monochromatic non-crossing paths, of length $\lceil\frac{n+1}{2}\rceil$. This bound cannot be improved. We also discuss some related problems and generalizations. In particular, we give sharp estimates for the largest number of disjoint monochromatic triangles that can always be selected from our segments. %A Khachiyan, Leonid %A Porkolab, Lorant %T Computing Integral Points in Convex Semi-algebraic Sets %D April 10, 1997 %Z Tue, 15 Apr 1997 19:46:12 GMT %I DIMACS %R 97-14 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-14.ps.gz %X Let $Y$ be a convex set in $R^k$ defined by polynomial inequalities and equations of degree $d \ge 2$ with integer coefficients of binary length $l$. We show that if $Y \cap Z^k \ne \emptyset$, then $Y$ contains an integral point of binary length $ld^{O(k^4)}$. For fixed $k$, our bound implies a polynomial-time algorithm for computing an integral point $y \in Y$. In particular, we extend Lenstra's theorem on the polynomial-time solvability of linear integer programming in fixed dimension to semidefinite integer programming. %A Reiter, Michael K. %A Rubin, Aviel D. %T Crowds: Anonymity for Web Transactions %D April 15, 1997 %Z Thu, 16 Jun 1997 19:20:23 GMT %I DIMACS %R 97-15 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-15new.ps.gz %X In this announcement we introduce a system called Crowds for protecting users' anonymity on the world-wide-web. Crowds, named for the notion of ``blending into a crowd'', operates by grouping users into a large and geographically diverse group (crowd) that collectively issues requests on behalf of its members. Web servers are unable to learn the true source of a request because it is equally likely to have originated from any member of the crowd, and indeed collaborating crowd members cannot distinguish the originator of a request from a member who is merely forwarding the request on behalf of another. Our security analysis introduces {\em degrees of anonymity} as an important tool for describing and proving anonymity properties. %A Muchnik, Ilya %A Mottl, Vadim %T Optimization algorithms for separable functions with tree-like adjacency of variables and their application to the analysis of massive data sets %D April 17, 1997 %Z Thu, 24 Apr 1997 23:45:56 GMT %I DIMACS %R 97-16 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-16.ps.gz %X A massive data set is considered as a set of experimentally acquired values of a number of variables each of which is associated with the respective node of an unoriented conjugacy graph that presets the fixed structure of the data set. The class of data analysis problems under consideration is outlined by the assumption that the ultimate aim of processing can be represented as a transformation of the original data array into a secondary array of the same structure but with node variables of, generally speaking, different nature, i.e. different ranges. Such a generalized problem is set as the formal problem of optimization (minimization or maximization) of a real-valued objective function of all the node variables. The objective function is assumed to consist of additive constituents of one or two arguments, respectively, node and edge functions. The former of them carry the data-dependent information on the sought-for values of the secondary variables, whereas the latter ones are meant to express the a priori model constraints. For the case when the graph of the pair-wise adjacency of the data set elements has the form of a tree, an effective global optimization procedure is proposed which is based on a recurrent decomposition of the initial optimization problem over all the node variables into a succession of partial problems each of which consists in optimization of a function of only one variable like Bellman functions in the classical dynamic programming. Two kinds of numerical realization of the basic optitimization procedure are considered on the basis of parametrical representation of Bellman functions, respectively, for discretely defined and quadratic node and edge functions. The proposed theoretical approach to the analysis of massive data sets is illustarted with its applications to the problems of the analysis of long molecular sequences and large visual images. %A Erdos, Peter L. %A Steel, Michael A. %A Szekely, Laszlo A. %A Warnow, Tandy J. %T Constructing big trees from short sequences %D May 6, 1997 %Z Tue, 6 May 1997 19:20:21 GMT %R 97-17 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-17.ps.gz %X The construction of evolutionary trees is a fundamental problem in biology, and yet methods for reconstructing evolutionary trees are not reliable when it comes to inferring accurate topologies of large divergent evolutionary trees from realistic lengh sequences. We address this problem and present a new polynomial time algorithm for reconstructing evolutionary trees called the Short Quartets Method which is consistent and which has greater statistical power than other polynomial time methods, such as Neighbor-Joining and the 3-approximation algorithm by Agarwala et al. (and the "Double Pivot" variant of the Agarwala et al. algorithm by Cohen and Farach) for the $L_{\infty}$-nearest tree problem. Our study indicates that our method will produce the correct topology from shorter sequences than can be guranteed using these other methods. %A DasGupta, Bhaskar %A He, Xin %A Jiang, Tao %A Li, Ming %A Tromp, John %T On the Linear-Cost Subtree-Transfer Distance between Phylogenetic Trees %D May 9, 1997 %Z Mon, 12 May 1997 17:23:13 GMT %R 97-18 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-18.ps.gz %X Different phylogenetic trees for the same group of species are often produced either by procedures that use diverse optimality criteria [14] or from different genes [10] in the study of molecular evolution. Comparing these trees to find their similarities and dissimilarities (i.e. distance) is thus an important issue in computational molecular biology. Several distance metrics including the nearest neighbor interchange (nni) distance and the subtree-transfer distance have been proposed and extensively studied in the literature. This article considers a natural extension of the subtree-transfer distance, called the linear-cost subtree-transfer distance, and studies the complexity and efficient approximation algorithms for this distance as well as its relationship to the nni distance. The linear-cost subtree-transfer model seems more logical than the (unit-cost) subtree-transfer model in some applications. The following is a list of our results.

1. The linear-cost subtree-transfer distance is in fact identical to the nni distance on unweighted phylogenies.

2. There is an algorithm to compute an optimal linear-cost subtree-transfer sequence between unweighted phylogenies in O(n^2 log n + n 2^{O(d)}) time, where d denotes the linear-cost subtree-transfer distance. Such an algorithm is usual when d is small.

3. Computing the linear-cost subtree-transfer distance between two weighted phylogenetic trees is NP-hard, provided we allow multiple leaves of a tree to share the same label (i.e. the trees are not necessarily uniquely labeled).

4. There is an efficient approximation algorithm for computing the linear-cost subtree-transfer distance between weighted phylogenies with performance ratio 2. %A Kayll, P. Mark %T Asymptotics of the total chromatic number for multigraphs %D May 14, 1997 %Z Thu, 22 May 1997 21:15:51 GMT %R 97-19 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-19.ps.gz %X or loopless multigraphs, the total chromatic number is asymptotically its fractional counterpart as the latter invariant increases without bound. This extends DIMACS Technical Report 96-20, where the same assertion, restricted to simple graphs, was proved. The proof for multigraphs --- presented in this note --- is based on a recent theorem, due to Kahn, establishing the analogous asymptotic behaviour of the list-chromatic index.

FOOTNOTE

This note is a companion article to DIMACS Technical Report 96-20. %A Blass, Andreas %A Gurevich, Yuri %A Shelah, Saharon %T Choiceless polynomial time %D June 2, 1997 %Z Mon, 2 Jun 1997 19:09:53 GMT %I DIMACS %R 97-20 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-20.ps.gz %X Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model whose machines do not distinguish between isomorphic structures and compute exactly PTime properties? This question can be recast as follows: Does there exist a logic that captures polynomial time (without presuming the presence of a linear order)? Earlier, one of us conjectured the negative answer. The problem motivated a quest of stronger and stronger PTime logics. All these logics avoid arbitrary choice. Here we attempt to capture the choiceless fragment of PTime. Our computation model is a version of abstract state machines (formerly called evolving algebras). The idea is to replace arbitrary choice with parallel execution. The resulting logic is more expressive than other PTime logics in the literature. A more difficult theorem shows that the logic does not capture all PTime. %A Lisitsa, Alexei %A Sazonov, Vladimir %T Bounded Hyperset Theory and Web-like Data Bases %D June 6, 1997 %Z Mon, 9 Jun 1997 20:58:01 GMT %I DIMACS %R 97-21 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-21.ps.gz %X It is demonstrated how a Hyperset Theory (satisfying P.Aczel's Anti-Foundation Axiom) naturally arises from the idea of World-Wide Web (WWW). Alternatively, Web serves as an illustration and possible application of the abstract notion of antifounded sets. A $\Delta$-language of Bounded Hyperset Theory is presented as a query language to the Web or, more generally, to Web-like Data Bases (WDB). It is shown that it describes exactly all abstract (or generic, up to bisimulation) PTIME-computable queries with respect to (possibly cyclic) graph encoding of hypersets. This result is based (i) on reducing of the $\Delta$-language for hypersets to the language FO+LFP ( = First-Order Logic with the Least Fixed-Point operator) over graphs considered up to bisimulation relation and (ii) on definability in FO+LFP of a linear ordering on any strongly extensional finite graph by a single formula (cf.\ also DIMACS TR-97-05). The case of finitely branching, possibly infinite graphs and corresponding hypersets is also discussed. It corresponds to finitely-branching, but infinite Web. However, it deserves special further investigation. %A Valtr, Pavel %T Graph drawings with no k pairwise crossing edges %D June 10, 1997 %Z Wed, 11 Jun 1997 22:39:24 GMT %I DIMACS %R 97-22 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-22.ps.gz %X A geometric graph is a graph $G=(V,E)$ drawn in the plane so that the vertex set $V$ consists of points in general position and the edge set $E$ consists of straight line segments between points of $V$. It is known that, for any fixed $k$, any geometric graph $G$ on $n$ vertices with no $k$ pairwise crossing edges contains at most $O(n log n)$ edges. In this paper we give a new, simpler proof of this bound, and show that the same bound holds also when the edges of $G$ are represented by $x$-monotone curves (Jordan arcs). %A Vanderbei, Robert J. %T Extension of Piyavskii's Algorithm to Continuous Global Optimization %D June 24, 1997 %Z Mon, 30 Jun 1997 22:50:12 GMT %I DIMACS %R 97-23 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-23.ps.gz %X We use the simple, but little-known, result that a uniformly continuous function on a convex set is $\epsilon$-Lipschitz (as defined below) to extend Piyavskii's algorithm for Lipschitz global optimization to the larger domain of continuous (not-necessarily-Lipschitz) global optimization. %A Kagan, Abram %A Mallows, Colin %A Shepp, Larry %A Vanderbei, Robert J. %A Vardi, Yehuda %T Symmetrization of Binary Random Variables %D June 24, 1997 %Z Mon, 30 Jun 1997 23:30:12 GMT %I DIMACS %R 97-24 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-24.ps.gz %X A random variable $Y$ is called an {\em independent symmetrizer} of a given random variable $X$ if (a) it is independent of $X$ and (b) the distribution of $X+Y$ is symmetric about $0$. In cases where the distribution of $X$ is symmetric about its mean, it is easy to see that the constant random variable $Y = - \Exp X$ is a minimum-variance independent symmetrizer. Taking $Y$ to have the same distribution as $-X$ clearly produces a symmetric sum but it may not be of minimum variance. We say that a random variable $X$ is {\em symmetry resistant} if the variance of any symmetrizer, $Y$, is never smaller than the variance of $X$. Let $X$ be a binary random variable: $\Prob \{ X = a \} = p$ and $\Prob \{ X = b \} = q$ where $a \ne b$, $0 < p < 1$, and $q = 1-p$. We prove that such a binary random variable is symmetry resistant if (and only if) $p \ne 1/2$. Note that the minimum variance as a function of $p$ is discontinuous at $p = 1/2$. Dropping the independence assumption, we show that the minimum-variance reduces to $pq - \min (p,q)/2$, which is a continuous function of $p$. %A Alon, Noga %A Dietzfelbinger, Martin %A Miltersen, Peter Bro %A Petrank, Erez %A Tardos, Gabor %T Linear Hashing %D June 27, 1997 %Z Mon, 3 Jul 1997 17:34:00 GMT %I DIMACS %R 97-25 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-25.ps.gz %X

Consider the set ${\cal H}$ of all linear (or affine) transf ormations between two vector spaces over a finite field $F$. We study how good $\cal H$ is as a class of hash functions, namely we consider hashing a set $S$ of size $n$ into a range having the same cardinali ty $n$ by a randomly chosen function from ${\cal H}$ and look at the expected size of the largest hash bucket. $\cal H$ is a universal class of hash functions for any fini te field, but with respect to our measure different fields behave differen tly.

If the finite field $F$ has $n$ elements then there is a bad set $S\subset F^2$ of size $n$ with expected maximal bucket size $\Omega(n^{1/3})$. If $n$ is a perfect square then there is even a bad set with largest bucket size {\em always} at least $\sqrt n$. (This is worst possible, since with respect to a universal class of hash functions every set of size $n$ has expected largest bucket size below $\sqrt n+1/2$.)

If, however, we consider the field of two elements then we get much better bounds. The best previously known upper bound on the expected size of the largest bucket for this class was $O( 2^{\sqrt{\log n}})$. We reduce this upper bound to $O(\log n\log\log n)$. Note that this is not far from the guarantee for a random function. There, the average largest bucket would be $\Theta(\log n/\log \log n)$.

In the course of our proof we develop a tool which may be of independent interest. Suppose we have a subset $S$ of a vector space $D$ over ${\bf Z}_2$, and consider a random linear mapping of $D$ to a smaller vector space $R$. If the cardinality of $S$ is larger than $c_\e|R|\log|R|$ then with probability $1-\e$, the image of $S$ will cover all elements in the range. %A Petrank, Erez %A Rackoff, Charles %T CBC MAC for Real-Time Data Sources %D June 27, 1997 %Z Mon, 3 Jul 1997 17:34:00 GMT %I DIMACS %R 97-26 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-26.ps.gz %X The Cipher Block Chaining (CBC) Message Authentication Code (MAC) is an authentication method which is widely used in practice. It is well known that the naive use of CBC MAC for variable length messages is not secure, and a few thumb rules for the correct use of CBC MAC are known by ``folklore''. The first rigorous proof of the security of CBC MAC, when used on fixed length messages, was given only recently by Bellare, Kilian and Rogaway \cite{bkr}. They also suggested variants of CBC MAC that handle variable length messages but in these variants the length of the message has to be known in advance (i.e., before the message is processed). \par We study CBC authentication of real time applications in which the length of the message is not known until the message ends, and furthermore, since the application is real-time, it is not possible to start processing the authentication only after the message ends. Providing authentication for real time communication is an important task, which involves authenticating real time speech transmissions, real time camera source of video transmission, and other human-driven multi media interaction. This also involves fax transmissions, in which the number of pages is not known in advance, and we would like to send the authentication as soon as the last page has been fed into the machine. \par We first present a variant of CBC MAC, called {\em double MAC} (DMAC) which handles messages of variable unknown lengths. Computing DMAC on a message is virtually as simple and as efficient as computing the standard CBC MAC on the message. We provide a rigorous proof that its security is implied by the security of the underlying block cipher. Next, we argue that the basic CBC MAC is secure when applied to prefix free message space. A message space can be made prefix free by authenticating also the (usually hidden) last character which marks the end of the message. %A Kilian, Joe %A Petrank, Erez %A Tardos, Gabor %T Probabilistically Checkable Proofs with Zero Knowledge %D June 27, 1997 %Z Mon, 3 Jul 1997 17:34:00 GMT %I DIMACS %R 97-27 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-27.ps.gz %X We construct PCPs with strong zero-knowledge properties. First, we construct polynomially bounded (in size) PCP's for {\sf NP} which can be checked using poly-logarithmic queries, with polynomially low error, yet are statistical zero-knowledge against an adversary that makes $U$ arbitrary queries, where $U$ can be set to any polynomial. Second, we construct PCPs for {\sf{NEXPTIME}} that can be checked using polynomially many queries, yet are statistically zero-knowledge against any polynomially bounded adversary. These PCPs are exponential in size and have exponentially low error. Previously, it was only known how to construct zero-knowledge PCPs with a constant error probability. \par In the course of constructing these PCP's we abstract a tool we call {\em locking systems}. We provide the definition and also a locking system with very efficient parameters. This mechanism may be useful in other settings as well. %A Kilian, Joe %A Petrank, Erez %T Identity Escrow %D June 27, 1997 %Z Mon, 3 Jul 1997 17:34:00 GMT %I DIMACS %R 97-28 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-28.ps.gz %X We introduce the notion of {\em escrowed identity}, an application of key-escrow ideas to the problem of identification. In escrowed identity, one party $A$ does {\em not} give his identity to another party $B$, but rather gives him information that would allow an authorized third party $E$ to determine $A$'s identity. However, $B$ receives a guarantee that $E$ can indeed determine $A$'s identity. We give protocols for escrowed identity based on the El-Gamal (signature and encryption) schemes and on the RSA function. A useful feature of our protocol is that after setting up $A$ to use the system, $E$ is only involved when it is actually needed to determine $A$'s identity. %A Krivelevich, Michael %A Sudakov, Benny %T The chromatic numbers of random hypergraphs %D June 29, 1997 %Z Mon, 2 Jul 1997 21:03:00 GMT %I DIMACS %R 97-29 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-29.ps.gz %X For a pair of integers 0 < t < r, the t-chromatic number of an r-uniform hypergraph H=(V,E) is the minimal k, for which there exists a partition of V into color classes U1,...,Uk such that every edge of H intersects every color class in at most t vertices. In this paper we determine the asymptotic behavior of the t-chromatic number of the random r-uniform hypergraph on n vertices with edge probability p=p(n) for all possible values of t and for a wide range of values of p. %A Derrida, B. %A Lebowitz, J. L. %A Speer, E. R. %T Shock Profiles for the Asymmetric Simple Exclusion Process in One Dimension %D July 2, 1997 %Z Mon, 7 Jul 1997 16:27:00 GMT %I DIMACS %R 97-30 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-30.ps.gz %X The asymmetric simple exclusion process (ASEP) on a one-dimensional lattice is a system of particles which jump at rates $p$ and $1-p$ (here $p>1/2$) to adjacent empty sites on their right and left respectively. The system is described on suitable macroscopic spatial and temporal scales by the inviscid Burgers' equation; the latter has shock solutions with a discontinuous jump from left density $\rho_-$ to right density $\rho_+$, $\rho_-<\rho_+$, which travel with velocity $(2p-1)(1-\rho_+-\rho_-)$. In the microscopic system we may track the shock position by introducing a second class particle, which is attracted to and travels with the shock. In this paper we obtain the time invariant measure for this shock solution in the ASEP, as seen from such a particle. The mean density at lattice site $n$, measured from this particle, approaches $\rho_{\pm}$ at an exponential rate as $n\to\pm\infty$, with a characteristic length which becomes independent of $p$ when $p/(1-p)>\sqrt{\rho_+(1-\rho_-)/\rho_-(1-\rho_+)}$. For a special value of the asymmetry, given by $p/(1-p)=\rho_+(1-\rho_-)/\rho_-(1-\rho_+)$, the measure is Bernoulli, with density $\rho_-$ on the left and $\rho_+$ on the right. In the weakly asymmetric limit, $2p-1\to0$, the microscopic width of the shock diverges as $(2p-1)^{-1}$. The stationary measure is then essentially a superposition of Bernoulli measures, corresponding to a convolution of a density profile described by the viscous Burgers equation with a well-defined distribution for the location of the second class particle. %A Toth, Geza %A Valtr, Pavel %T Note on the Erdos-Szekeres theorem %D July 4, 1997 %Z Fri, 11 Jul 1997 19:20:15 GMT %I DIMACS %R 97-31 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-31.ps.gz %X Let $g(n)$ denote the least integer such that among any $g(n)$ points in general position in the plane there are always $n$ in convex position. In 1935 P. Erd\H os and G. Szekeres showed that $g(n)$ exists and $2^{n-2}+1\le g(n)\le {2n-4\choose n-2}+1$. Recently, the upper bound has been slightly improved by Chung and Graham and by Kleitman and Pachter. In this note we further improve the upper bound to $$g(n)\le {2n-5\choose n-2}+2.$$ %A Beimel, Amos %A Kushilevitz, Eyal %T Learning Boxes in High Dimension %D June 27, 1997 %Z Fri, 11 Jul 1997 19:20:15 GMT %I DIMACS %R 97-32 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-32.ps.gz %X We present exact learning algorithms that learn several classes of (discrete) boxes in $\{0,\ldots,\ell-1\}^n$. In particular we learn: (1) The class of unions of $O(\log n)$ boxes in time $\poly(n,\log\ell)$ (solving an open problem of \cite{GGM94,BGGM94}; in~\cite{BBBKV97} this class is shown to be learnable in time $\poly(n,\ell)$). (2) The class of unions of disjoint boxes in time $\poly(n,t,\log\ell)$, where $t$ is the number of boxes. (Previously this was known only in the case where all boxes are disjoint in one of the dimensions; in~\cite{BBBKV97} this class is shown to be learnable in time $\poly(n,t,\ell)$). In particular our algorithm learns the class of decision trees over $n$ variables, that take values in $\{0,\ldots,\ell-1\}$, with comparison nodes in time $\poly(n,t,\log\ell)$, where $t$ is the number of leaves (this was an open problem in \cite{Bsh93} which was shown in \cite{BBBKV96} to be learnable in time $\poly(n,t,\ell)$). (3) The class of unions of $O(1)$-degenerate boxes (that is, boxes that depend only on $O(1)$ variables) in time $\poly(n,t,\log\ell)$ (generalizing the learnability of $O(1)$-DNF and of boxes in $O(1)$ dimensions). The algorithm for this class uses only equivalence queries and it can also be used to learn the class of unions of $O(1)$ boxes (from equivalence queries only). %A Farach, Martin %A Liberatore, Vincenzo %T On Local Register Allocation %D July 11, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-33 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-33.ps.gz %X

In this paper, we consider the problem of Local Register Allocation (LRA): given a sequence of instructions (basic block) and a number of general purpose registers, find the schedule of variables in registers that minimizes the total traffic between CPU and the memory system. Local register allocation has been studied for more than thirty years in the theory and compiler communities.

It was not known if LRA is NP-hard, but no subexponential time algorithm was known. Furthermore, the most popular heuristics in use in compilers can perform arbitrarily poorly in the worst case. In this paper, we present the following results:

We report the experimental performance of a branch-and-bound algorithm and both approximation algorithms on standard benchmarks. %A Boros, Endre %A Cepek, Ondrej %A Kogan, Alexander %T Horn Minimization by Iterative Decomposition %D July 11, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-34 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-34.ps.gz %X The problem of Horn minimization can be stated as follows: given a Horn CNF representing a Boolean function $f$, find a CNF representation of $f$ which consists of a minimum possible number of clauses. This problem is the formalization of the problem of knowledge compression for speeding up queries to propositional Horn expert systems, and it is known to be NP-hard. In this paper we present a linear time algorithm which takes a Horn CNF as an input, and through a series of decompositions reduces the minimization of the input CNF to the minimization problem on a ``shorter" CNF. The correctness of this decomposition algorithm rests on several interesting properties of Horn functions which, as we prove here, turn out to be independent of the particular CNF representations. %A Spencer, Joel %A Thoma, Lubos %T On the Limit Values of Probabilities for the First Order Properties of Graphs %D July 21, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-35 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-35.ps.gz %X Consider the random graph ${\cal G}(n,p),$ where $p=p(n)$ is any threshold function satisfying $p(n) = \Theta(\ln n / n).$ We give a full characterization of the limit values of probabilities of ${\cal G}(n,p)$ having a property $\psi,$ where $\psi$ is any sentence of the first order theory of graphs. %A Fang, Weiwu %T FDOD Function and the Information Discrepancy Contained in Multiple Probability Distributions %D July 23, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-36 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-36.ps.gz %X

The concept of Shonnon information has played a significant role in a variety of scientific and engineering areas. The question naturally arises: how can we measure information discrepancy contained in two or more probability distributions? The answer to this problem will be very interesting in both theory and practice. Some measures for the cases of two or three distributions have presented by the pioneers, but these measures have some disadvantages; moreover, there doesn't exist a measure for $n$ distributions so far.

A FDOD function with many good properties has been introduced in the study of information discrepancy of judgments of multiple experts ( FW 1994). In this paper, based on the ideas concerned with Shannon information and measures of difference, we propose an axiom set for measuring the information discrepancy contained in a group of distributions, and prove that the only function satisfying the axiom set is of the FDOD form. The final results and even the intermediate results in deed show the close connection of the FDOD function with Shannon information and the measures of difference in statistics. %A Muramatsu,Masakazu %A Vanderbei, Robert J. %T Affine Scaling Algorithms Fail for Semidefinite Programming %D July 25, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-37 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-37.ps.gz %X In this paper, we give an example of a semidefinite programming problem in which primal-dual affine-scaling algorithms using the XZ, MT, and AHO directions fail. We prove that each of these algorithm can generate a sequence converging to a non-optimal solution, and that, for the AHO direction, even its associated continuous trajectory can converge to a non-optimal point. In contrast with these directions, we show that the primal-dual affine-scaling algorithm using the NT direction for the same semidefinite programming problem always generates a sequence converging to the optimal solution. Both primal and dual problems have interior feasible solutions, unique optimal solutions which satisfy strict complementarity, and are nondegenerate everywhere. %A Lo, Eddie H. %A Ostheimer, Gretchen %T A Practical Algorithm for Finding Matrix Representations for Polycyclic Groups %D August 10, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-38 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-38.ps.gz %X We describe a new algorithm for finding matrix representations for polycyclic groups given by finite presentations. In contrast to previous algorithms, our algorithm is efficient enough to construct representations for some interesting examples. The examples which we studied included a collection of free nilpotent groups, and our results here led us to a theoretical result concerning such groups. %A Grunewald, Stefan %A Steffen, Eckhard %T Chromatic-Index Critical Graphs of Even Order %D August 21, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-39 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-39.ps.gz %X

A $k$-critrical graph $G$ has maximum degree $k \geq 0$, chromatic index $\chi'(G) = k+1$ and $\chi'(G-e) < k+1$ for each edge $e$ of $G$.

The Critical Graph Conjecture independently stated by I.T. Jakobsen (On critical graphs with chromatic index 4, Disc. Math. 9 (1974) 265-276), and L. W. Beineke, R. J. Wilson (On the edge chromatic number of a graph, Disc. Math. 5 (1973) 15-20) claims that every $k$-critical graph is of odd order. S. Fiorini, R. J. Wilson (Edge-colourings of graphs, in L. W. Beineke, R. J. Wilson (eds.) Selected Topics in Graph Theory, Academic Press London (1978) 103-126) conjectured that every $k$-critical graph of even order has a 1-factor. A. G. Chetwynd and H. P. Yap (Chromatic index critical graphs of order 9, Disc. Math. 47 (1983) 23-33) stated the problem whether it is true that if $G$ is a $k$-critical graph of odd order, then $G-v$ has a 1-factor for every vertex $v$ of minimum degree. These conjectures are disproved and the problem is answered in the negative for $k \in \{3,4\}$.

We disprove these conjectures and answer the problem in the negative for all $k \geq 3$.

We also construct $k$-critical graphs on $n$ vertices with degree sequence $23^24^{n-3}$, answering a question of Yap (Some topics in graph theory, London Math.~Soc.~LNS 108, Cambridge University Press (1986)). %A Allender, Eric %A Beals, Robert %A Ogihara, Mitsunori %T The Complexity of Matrix Rank and Feasible Systems of Linear Equations %D August 27, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-40 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-40.ps.gz %X

We characterize the complexity of some natural and important problems in linear algebra. In particular, we identify natural complexity classes for which the problems of (a) determining if a system of linear equations is feasible and (b) computing the rank of an integer matrix, (as well as other problems), are complete under logspace reductions.

As an important part of presenting this classification, we show that the ``exact counting logspace hierarchy'' collapses to near the bottom level. (We review the definition of this hierarchy below.) We further show that this class is closed under NC^1-reducibility, and that it consists of exactly those languages that have logspace uniform span programs (introduced by Karchmer and Wigderson) over the rationals.

In addition, we contrast the complexity of these problems with the complexity of determining if a system of linear equations has an integer solution. %A Beimel, Amos %A Franklin, Matthew %T Reliable Communication over Partially Authenticated Networks %D August 28, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-41 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-41.ps.gz %X Reliable communication between parties in a network is a basic requirement for executing any protocol. In this work, we consider the effect on reliable communication when some pairs of parties have common authentication keys. The %%%distribution of pairs sharing keys define a natural ``authentication graph'', which may be quite different from the ``communication graph'' of the network. We characterize when reliable communication is possible in terms of these two graphs, focusing on the very strong setting of a Byzantine adversary with unlimited computational resources. %A DIMACS %T Proceedings of Third DIMACS Workshop on DNA Based Computers %D June 23, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-42 %U http://dimacs.rutgers.edu/Workshops/DNA3/index.html %X Proceedings of Third DIMACS Workshop on DNA Based Computers %A DIMACS %T DIMACS Workshop on Design and Formal Verification of Security Protocols %D September 3, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-43 %U http://dimacs.rutgers.edu/Workshops/Security/index.html %X DIMACS Workshop on Design and Formal Verification of Security %A Ostheimer, Gretchen %T Practical Algorithms for Polycyclic Matrix Groups %D September 7, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-44 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-44.ps.gz %X Many fundamental problems are undecidable for infinite matrix groups. Polycyclic matrix groups represent a large class of groups for which these same problems are known to be decidable. In this paper we describe a suite of new algorithms for studying polycyclic matrix groups --- algorithms for testing membership and for uncovering the polycyclic structure of the group. We also describe an algorithm for deciding whether or not a group is solvable, which, in the important context of subgroups of GL(n,Z), is equivalent to deciding whether or not a group is polycyclic. In contrast to previous algorithms, the algorithms in this paper are practical: experiments show that they are efficient enough to be useful in studying some reasonably complex examples using current technology. %A Allender, Eric %T Some Pointed Questions Concerning Asymptotic Lower Bounds %D September 8, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-45 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-45.ps.gz %X This column was originally written to appear in the Bulletin of the EATCS. In this column, I survey some aspects of complexity theory that can hardly be considered ``recent''. Instead, I will focus on some fundamental truths relating complexity theory to practical computing. These truths deserve repeating, lest they become forgotten. %A Reinhardt, Klaus %A Allender, Eric %T Making Nondeterminism Unambiguous %D September 8, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-46 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-46.ps.gz %X We show that in the context of nonuniform complexity, nondeterministic logarithmic space bounded computation can be made unambiguous. An analogous result holds for the class of problems reducible to context-free languages. In terms of complexity classes, this can be stated as: NL/poly = UL/poly LogCFL/poly = UAuxPDA(log n, poly)/poly %A Mundhenk, Martin %A Goldsmith, Judy %A Lusena, Christopher %A Allender, Eric %T Encyclopaedia of Complexity Results for Finite-Horizon Markov Decision Process Problems %D September 8, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-47 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-47.ps.gz %X The computational complexity of finite horizon policy evaluation and policy existence problems are studied for several policy types and representations of Markov decision processes. In almost all cases, the problems are shown to be complete for their complexity classes; classes range from nondeterministic logarithmic space and probabilistic logarithmic space (highly parallelizable classes) to exponential space. In many cases, this work shows that problems that already were widely believed to be hard to compute are probably intractable (complete for NP, NP^PP , or PSPACE), or provably intractable (EXPTIME-complete or worse). The major contributions of the paper are to pinpoint the complexity of these problems; to isolate the factors that make these problems computationally complex; to show that even problems such as median-policy or average-policy evaluation may be intractable; and the introduction of natural NP^PP-complete problems. %A Agrawal, Manindra %A Allender, Eric %A Datta, Samir %T On TC^0, AC^0, and Arithmetic Circuits %D September 8, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-48 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-48.ps.gz %X Continuing a line of investigation that has studied the function classes #P, #SAC^1, #L, and #NC^1, we study the class of functions #AC^0. One way to define #AC^0 is as the class of functions computed by constant-depth polynomial-size arithmetic circuits of unbounded fan-in addition and multiplication gates. In contrast to the preceding function classes, for which we know no nontrivial lower bounds, lower bounds for #AC^0 follow easily from established circuit lower bounds.

One of our main results is a characterization of TC^0 in terms of #AC^0: A language A is in TC^0 if and only if there is a #AC^0 function f and a number k such that x is in A iff f(x) = 2^|x|^k. Using the naming conventions of this area of research, this yields: TC^0 = PAC^0 = C=AC^0

Another restatement of this characterization is that TC^0 can be simulated by constant-depth arithmetic circuits, with a single threshold gate. We hope that perhaps this characterization of TC^0 in terms of AC^0 circuits might provide a new avenue of attack for proving lower bounds.

Our characterization differs markedly from earlier characterizations of TC^0 in terms of arithmetic circuits over finite fields. Using our model of arithmetic circuits, computation over finite fields yields ACC.

We also prove a number of closure properties and normal forms for #AC^0. %A Allender, Eric %T Circuit Complexity before the Dawn of the New Millennium %D September 8, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-49 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-49.ps.gz %X The 1980's saw rapid and exciting development of techniques for proving lower bounds in circuit complexity. This pace has slowed recently, and there has even been work indicating that quite different proof techniques must be employed to advance beyond the current frontier of circuit lower bounds. Although this has engendered pessimism in some quarters, there have in fact been many positive developments in the past few years showing that significant progress is possible on many fronts. This paper is a (necessarily incomplete) survey of the state of circuit complexity as we await the dawn of the new millennium. %A Allender, Eric %A Lange, Klaus-Joern %T RUSPACE(log n) is contained in DSPACE(log^2 n / loglog n) %D September 8, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-50 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-50.ps.gz %X We present a deterministic algorithm running in space O(log^2 n/ loglog n) solving the connectivity problem on strongly unambiguous graphs. In addition, we present an O(log n) time-bounded algorithm for this problem running on a parallel pointer machine. %A Allender, Eric %T The Permanent Requires Large Uniform Threshold Circuits %D September 8, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-51 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-51.ps.gz %X A recent paper by Caussinus, McKenzie, Therien, and Vollmer shows that there are problems in the counting hierarchy that require superpolynomial-size uniform TC^0 circuits. Their proof uses ``leaf languages'' as a tool in obtaining their separations, and their proof does not immediately yield larger lower bounds for the complexity of these problems, and it also does not yield a lower bound for any particular problem at any fixed level of the counting hierarchy. (It only shows that hard problems must exist at some level.) In this paper, we give a simple direct proof, showing that any problem that is hard for the complexity class C_=P requires more than size T(n), if for all k, T^{(k)}(n) = o(2^n). Thus, in particular, the permanent, and any problem hard for PP or #P require circuits of this size. Related and somewhat weaker lower bounds are also presented, extending the theorem of (Caussinus et al.) showing that ACC^0 is properly contained in ModPH. %A Fredman, Michael L. %T Pairing Heaps Are Suboptimal %D September 8, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-52 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-52.ps.gz %X Pairing heaps were introduced as a self-adjusting alternative to Fibonacci heaps. They provably enjoy log n amortized costs for the standard heap operations. Although it has not been verified that pairing heaps perform the decrease key operation in constant amortized time, this has been conjectured and extensive experimental evidence supports this conjecture. Moreover, pairing heaps have been observed to be superior to Fibonacci heaps in practice. However, as demonstrated in this paper, pairing heaps do not accommodate decrease key operations in constant amortized time. %A Dreyer, Paul A. Jr. %A Biedl, Therese C. %T Rectangle Breaking in Grids %D September 8, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-53 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-53.ps.gz %X Given an $n \times n$ square grid, there are the outlines of $n^2$ $1 \times 1$ squares, $(n-1)^2$ $2 \times 2$ squares, and so on. What is the minimum number of edges that can be removed from the grid such that there is no complete outline of a square remaining? Using techniques from tiling problems and other graph theoretic methods, we solve the problem for all $n$ and prove similar results for rectangular grids for which the side lengths differ by no more than six. We also introduce another version of the problem where we ask for the minimum number of edges to ``break'' all of the rectangles in a grid. %A Kolaitis, Phokion %T Special Year on Logic and Algorithms Tutorial Notes: Expressive Powers of Logics (Tutorial Lectures by Phokion Kolaitis) %D September 8, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-54 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-54.ps.gz %X

The 1995-1996 DIMACS Special Year on Logic and Algorithms began with three week-long tutorial sessions on the topics of the special year:

These notes on the lectures given by Phokion Kolaitis were compiled by Eric Allender from the notes supplied by Randall J. Pruim, Brenda J. Latka, Jim Rogers, Maria-Luisa Bonet, and Kousha Etessami. %A Immerman, Neil %T Special Year on Logic and Algorithms Tutorial Notes: Descriptive Complexity (Tutorial Lectures by Neil Immerman) %D September 8, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-55 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-55.ps.gz %X

The 1995-1996 DIMACS Special Year on Logic and Algorithms began with three week-long tutorial sessions on the topics of the special year:

These notes on the lectures given by Neil Immerman were compiled by Eric Allender from the notes supplied by A. Arratia, Sandeep K. Shukla, J. Avigad, and D. Sivakumar. %A Lynch, James %T Special Year on Logic and Algorithms Tutorial Notes: Random Finite Models (Tutorial Lectures by James Lynch) %D September 8, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-56 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-56.ps.gz %X

The 1995-1996 DIMACS Special Year on Logic and Algorithms began with three week-long tutorial sessions on the topics of the special year:

These notes on the lectures given by James Lynch were compiled by Eric Allender from the notes supplied by Thomas Wilke, James Lynch, Sandeep K. Shukla, Helmut Veith, and Ida Pu. %A Kurshan, Robert %A Shukla, Sandeep %T Special Year on Logic and Algorithms Tutorial Notes: Complexity Issues in Automata-Theoretic Verification: The COSPAN Approach to Deal with These Issues(Tutorial Lectures by Robert Kurshan) %D September 8, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-57 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-57.ps.gz %X The 1995-1996 DIMACS Special Year on Logic and Algorithms began with three week-long tutorial sessions on the topics of the special year: Finite Model Theory Proof Complexity Computer-Aided Verification These notes on the lectures given by Robert Kurshan were compiled by Sandeep K. Shukla. %A Bacso, Gabor %A Boros, Endre %A Gurvich, Vladimir %A Maffray, Frederic %A Preissmann, Myriam %T On Minimally Imperfect Graphs with Circular Symmetry %D September 8, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-58 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-58.ps.gz %X Results of Lovász and Padberg entail that the class of so-called partitionable graphs contains all the potential counterexamples to Berge's famous Strong Perfect Graph Conjecture (which asserts that the only minimally imperfect graphs are the odd chordless cycles with at least five vertices and their complements). Only two constructions (due to Chvátal, Graham, Perold and Whitesides) are known for making partitionable graphs. The first one does not produce any counterexample to Berge's Conjecture, as shown by Sebö. Here we prove that the second construction does not produce any counterexample either. We conjecture that every partitionable graph with circular symmetry can be generated by this second construction, and give results in this direction. We also show that, regardless of this conjecture, every minimally imperfect graph with circular symmetry must have an odd number of vertices. %A Brinkmann, Gunnar %A Steffen, Eckhard %T Chromatic Index Critical Graphs of Orders 11 and 12 %D September 9, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-59 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-59.ps.gz %X A chromatic-index-critical graph $G$ on $n$ vertices is non-trivial if it has at most $\Delta \lfloor \frac{n}{2} \rfloor$ edges. We prove that there is no chromatic-index-critical graph of order 12, and that there are precisely two non-trivial chromatic index critical graphs on 11 vertices. Together with known results this implies that there are precisely three non-trivial chromatic-index-critical graphs of order $\leq 12$. %A Agrawal, Manindra %A Allender, Eric %A Rudich, Steven %T Reductions in Circuit Complexity: An Isomorphism Theorem and a Gap Theorem %D September 11, 1997 %Z Fri, 23 Jul 1999 20:00:00 GMT %I DIMACS %R 97-60 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-60.ps.gz %X We show that all sets that are complete for NP under non-uniform AC^0 reductions are isomorphic under non-uniform AC^0-computable isomorphisms. Furthermore, these sets remain NP-complete even under non-uniform NC^0 reductions. More generally, we show two theorems that hold for any complexity class C closed under (uniform) NC^1-computable many-one reductions. Gap: The sets that are complete for C under AC^0 and NC^0 reducibility coincide. Isomorphism: The sets complete for C under AC^0 reductions are all isomorphic under isomorphisms computable and invertible by AC^0 circuits of depth three. Our Gap Theorem does not hold for strongly uniform reductions: we show that there are Dlogtime-uniform AC^0-complete sets for NC^1 that are not Dlogtime-uniform NC^0-complete.} (This technical report replaces DIMACS TR 96-04.) %A Allender, Eric %A Arvind, V %A Mahajan, Meena %T Arithmetic Complexity, Kleene Closure, and Formal Power Series %D September 12, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-61 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-61.ps.gz %X

In this paper we show how two fundamental operations used in formal language theory provide useful tools for the investigation of arithmetic complexity classes. More precisely, we use Kleene closure of languages and inversion of formal power series to investigate subclasses of the complexity class GapL. GapL is the complexity class that characterizes the complexity of computing the determinant; it corresponds to counting the number of accepting and rejecting paths of nondeterministic logspace-bounded Turing machines.) We define a counting version of Kleene closure and show that it is intimately related to inversion within the complexity classes GapL and GapNC^1. In particular, we prove that Kleene closure and inversion are both hard operations in the following sense

Furthermore, we classify the complexity of the Kleene closure of finite languages. We formulate the problem in terms of finite monoids and relate its complexity to the internal structure of the monoid. %A Brightwell, Graham R. %A Winkler, Peter %T Graph Homomorphisms and Phase Transitions %D September 17, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-62 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-62.ps.gz %X We model physical systems with "hard constraints" by the space Hom(G,H) of homomorphisms from a locally finite graph G to a fixed finite constraint graph H. For any assignment $\lambda$ of positive real activities to the nodes of H, there is at least one Gibbs measure on Hom(G,H); when G is infinite, there may be more than one.

When G is a regular tree, the simple, invariant Gibbs measures on Hom(G,H) correspond to node-weighted branching random walks on H. we show that such walks exist for every H and $\lambda$, and characterize those H which, by admitting more than one such construction, exhibit phase transition behavior. %A Durand, D. %A Farach, M. %A Ravi, R. %A Singh, M. %T A Short Course in Computational Molecular Biology %D September 17, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-63 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-63.ps.gz %X The advent of recombinant DNA technology during the 1970s has led to an inundation of biological sequence data. The compilation and analysis of DNA and protein sequences is now a fundamental task in molecular biology requiring. Computational Molecular Biology is the field of computer science that has emerged to solve algorithmic problems in determining sequences and analyzing them. Specific research efforts in this area include sequencing and mapping, pairwise and multiple sequence comparison, protein structure determination and evolutionary tree reconstruction. Solutions to these problems contribute both to basic scientific research and product development in the biotechnology industry. We have designed a course to give a basic introduction to the major algorithmic research areas in computational biology. %A Malkhi, Dahlia %A Reiter, Michael %A Rubin, Avi %T The Design and Implementation of a Java Playground %D September 19, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-64 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-64.ps.gz %X Mobile code presents a number of threats to the machines that execute it. In this paper we introduce an approach for protecting machines and the resources they hold from mobile code, and describe a system based on our approach for protecting host machines from Java applets. In our approach, each Java applet downloaded to the protected domain is rerouted to a dedicated machine (or set of machines), the playground, at which it is executed. Prior to execution the applet is transformed to use the downloading user's web browser as a graphics terminal for its input and output, and so the user has the illusion that the applet is running on her own machine. In reality, however, mobile code runs only in the sanitized environment of the playground, where user files cannot be mounted and from which only limited network connections are accepted by machines in the protected domain. We describe the design, implementation, performance and limitations of our system, and directions for future work. %A Abbasi, Sarmad %T Longest Common Consecutive Substring in Two Random Strings %D October 7, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-65 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-65.ps.gz %X Let $\Sigma$ be a finite alphabet with $C$ letters. For any two strings $x$ and $y$ of length $n$, we let $S(x,y)$ denote the size of the longest common consecutive substring between $x$ and $y$; that is, $S(x,y)$ is the largest $k$ such that, $$ x_i \cdots x_{i+k} = y_j \cdots y_{j+k}$$ for some $i$ and $j$. We show that for $x$ and $y$ chosen uniformly among all possible strings of length $n$, $S(x,y)$ is highly concentrated around $2 \log_C n$. More precisely, for any $a \geq 1$ $$ \Pr [ |S(x,y) - 2 \log_C n | > a] \leq {18 C^{-a} \over n^2}.$$ This enables us to show that the expected value of $S(x,y)$ is with a constant additive factor of $2 \log n$. %A Pach, Janos %A Toth, Geza %T A Generalization of the Erdos-Szekeres Theorem to Disjoint Convex Sets %D October 13, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-66 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-66.ps.gz %X Let ${\cal F}$ denote a family of pairwise disjoint convex sets in the plane. ${\cal F}$ is said to be in {\em convex position}, if none of its members is contained in the convex hull of the union of the others. For any fixed $k\geq 3$, we estimate $P_k(n)$, the maximum size of a family ${\cal F}$ with the property that any $k$ members of ${\cal F}$ are in convex position, but no $n$ are. In particular, for $k=3$, we improve the triply exponential upper bound of T. Bisztriczky and G. Fejes T\'oth by showing that $P_3(n)<16^n$. %A Shepp, Larry %T Linear Programming in Tomography, Probability, and Finance %D October 15, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-67 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-67.ps.gz %X

At the first conference (at DIMACS), it became clear that linear, or convex, programming is going to play a key role in the algorithmics of "discrete tomography", where one attempts to reconstruct a finite subset, $S$, of the integer lattice, $Z^2$, or $Z^3$, from its line sums in a few directions obtained via transmission electron microscopy. The usual convolution-back-projection algorithms for continuous tomography are useless for this new application to crystal microscopy because only very few directions are available for which the line sums are measured. Since the problem of determining a subset $S$ with the given line sums is an integer programming problem the standard convexification of the problem reduces it to linear programming (Peter Fishburn, Peter Schwander, Robert Vanderbei, The Discrete Radon Transform and its Approximate Inversion via Linear programming, Discrete Applied Math., 1997, to appear). This showed that $S$ may be "effectively" reconstructed in the sense that the method of finding a feasible interior point in the convex hull of what is called "fuzzy sets", ie a function, $0 \le f(z) \le 1$ for all $z \in Z^2$, or $Z^3$, "typically" produces a reasonablly satisfactory reconstruction on simulated phantoms. Thus the situation is more or less analogous to conventional medical CT scanning, where even though one cannot hope to uniquely reconstruct a function, $f(x,y)$ from its line integrals in a finite number of fixed directions (even if the line integrals are noiseless) the usual algoorithms are seen to work well, as demonstrated via simulations.

In the above paper written over a year ago, available by request at fish@research.att.com, the method is made clear. Here however I have a different goal: several disparate problems in applied mathematics can be solved via non-trivial use of infinite linear programming and I thought that I would share these with the audience in order to illustrate the scope and the power of linear programming and to bring the ideas to wider view, after first trying to set into perspective the application of linear programming to discrete tomography via a review. %A Odlyzko, Andrew %T A Modest Proposal for Preventing Internet Congestion %D October 17, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-68 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-68.ps.gz %X A simple approach, called PMP (Paris Metro Pricing), is suggested for dealing with congestion in packet networks such as the Internet. It is to partition a network into several logical networks, each of which would treat all packets equally on a best effort basis, just as the current Internet does. There would be no formal guarantees of quality of service. The separate networks would differ only in the prices paid for using them. Networks with higher prices would attract less traffic, and thereby provide better service. Price would be the primary tool of traffic management. %A Liberatore, Vincenzo %T Uniform Multipaging Reduces to Paging %D October 15, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-69 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-69.ps.gz %X Multipaging is the paging problem when more than one page can be requested at each step. In the uniform cost model, a paging algorithm is charged for the number of pages loaded from disk to fast memory. In this note, we establish a general reduction from uniform multipaging to paging. As a consequence, we obtain the first strongly competitive randomized algorithm for uniform multipaging. %A Coffman, E. G. %A Flajolet, Philippe Jr. %A Leopold Flatto %A Micha Hofri %T The Maximum of a Random Walk and Its Application to Rectangle Packing %D October 15, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-70 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-70.ps.gz %X Let $S_0, \ldots ,S_n$ be a symmetric random walk that starts at the origin ($S_0=0$), and takes steps uniformly distributed on $[-1,+1]$. We study the large-$n$ behavior of the expected maximum excursion and prove the estimate \[ \exd \max_{0 \leq k \leq n} S_k = \sqrt{\frac{2n}{3\pi}} - c + \frac{1}{5}\sqrt{\frac{2}{3\pi}} n^{-1/2} + O(n^{-3/2}), \] where $c=0.297952\ldots$. This estimate applies to the problem of packing $n$ rectangles into a unit-width strip; in particular, it makes much more precise the known upper bound on the expected minimum height, $\frac{n}{4} + \frac{1}{2} \exd \max_{0 \leq j \leq n} S_j +\frac{1}{2} = \frac{n}{4} + O(n^{1/2}),$ when the rectangle sides are $2n$ independent uniform random draws from $[0,1]$. %A Erdos, P. L. %A Steel, M. A. %A Szekely, L. A. %A Warnow, T. J. %T A few logs suffice to build (almost) all trees (I) %D October 17, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-71 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-70.ps.gz %X A phylogenetic tree (also called an ``evolutionary tree'') is a leaf-labelled tree which represents the evolutionary history for a set of species, and the construction of such trees is a fundamental problem in biology. Here we address the issue of how many sequence sites are required in order to recover the tree with high probability when the sites evolve under standard Markov- style (i.i.d.) mutation models. We provide analytic upper and lower bounds for the required sequence length, by developing a new (and polynomial time) algorithm. In particular we show that when the mutation probabilities are bounded the required sequence length can grow surprisingly slowly (a power of log n) in the number n of sequences, for almost all trees. %A Erdos, P. L. %A Steel, M. A. %A Szekely, L. A. %A Warnow, T. J. %T A few logs suffice to build (almost) all trees (II) %D October 17, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-72 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-70.ps.gz %X Inferring evolutionary trees is an interesting and important problem in biology that is very difficult from a computational point of view as most associated optimization problems are NP-hard. Although it is known that many methods are provably statistically consistent (i.e. the probability of recovering the correct tree converges on 1 as the sequence length increases), the actual rate of convergence for different methods has not been well understood. In a recent paper we introduced a new method for reconstructing evolutionary trees called the Dyadic Closure Method (DCM), and we showed that DCM has a very fast convergence rate. DCM runs in O(n^5 log n) time, where n is the number of sequences, so although it is polynomial it has computational requirements that are potentially too large to be of use in practice. In this paper we present another tree reconstruction method, the Witness-Antiwitness Method, or WAM. WAM is significantly faster than DCM, especially on random trees, and converges at the same rate as DCM. We also compare WAM to other methods used to reconstruct trees, including Neighbor Joining (possibly the most popular method among molecular biologists), and new methods introduced in the computer science literature. %A Pach, Janos %A Thiele, Torsten %A Toth, Geza %T Three-dimensional Grid Drawings of Graphs %D October 28, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-73 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-70.ps.gz %X A three-dimensional {\em grid drawing} of a graph $G$ is a placement of the vertices at distinct integer points so that the straight-line segments representing the edges of $G$ are pairwise non-crossing. It is shown that for any fixed $r\geq 2$, every $r$-colorable graph of $n$ vertices has a three-dimensional grid drawing that fits into a box of volume $O(n^2)$. The order of magnitude of this bound cannot be improved. %A Muchnik, Andrei %A Romashchenko, Andrei %A Shen, Alexander %A Vereshagin, Nikolai %T Upper semi-lattice of binary strings with the relation ``x is simple conditional to y'' %D November 5, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-74 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-70.ps.gz %X We study the properties of the set of binary strings with the relation ``the Kolmogorov complexity of x conditional to y is small''. We prove that there are pairs of strings which have no greatest common lower bound with respect to this pre-order. We present several examples when the greatest common lower bound exists but its complexity is much less than mutual information (extending the Gacs and Koerner result). %A Foldes, Stephan %T On Automorphism Groups of Graphs and Distributive Lattices %D November 12, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-75 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-70.ps.gz %X Birkhoff's theorem that every group is isomorphic to the automorphism group of a distributive lattice is extended in a direction that parallels similar results in graph theory. %A Gruenewald, Stefan %A Steffen, Eckhard %T Cyclically 5-edge Connected Con-bicritical Critical Snarks %D November 17, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-76 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-70.ps.gz %X Snarks are bridgeless cubic graphs with chromatic index $\chi' = 4$. A snark $G$ is called critical if $\chi'(G-\{v,w\}) = 3$, for any two adjacent vertices $v$ and $w$. For any $k \geq 2$ we construct cyclically 5-edge connected critical snarks $G$ having an independent set $I$ of at least $k$ vertices such that $\chi'(G-I)=4$. For $k=2$ this solves a problem of Nedela and \v{S}koviera stated in "Decompositions and Reductions of Snarks" J. of Graph Th. 22 253-279 (1996). %A Jia, Ning %A Jia, Xiaofeng %T Some Results Concerning the Ends of Minimal Cuts of Simple Graphs %D November 21, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-77 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-70.ps.gz %X Let S be a cut of a simple connected graph G.If S has no proper subset that is a cut, we say S is a minimal cut of G. To a minimal cut S, a connected component of G-S is called a fragment. And a fragment with no proper subset that is also a fragment is called an end. We characterized ends in our discussions and proved that to a connected graph G=(V,E), the number of its ends<=|V(G)|. %A DasGupta, Bhaskar %T Remarks on the equivalence problem for PL-sets %D November 29, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-78 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-70.ps.gz %X The following problem arises in connection with checking the equivalence piecewise-linear (PL) sets. Consider two-variable polynomials with non-negative integer coefficients, and given two such polynomials, decide if they are equivalent to each other modulo the following equalities $x=2x+1$, $y^2=2y^2+y$ and $y=x+y+1$. In this paper, we show that this problem can be solved in polynomials time in both the unit-cost and the logarithmic-cost model. %A Ekin, Oya %A Foldes, Stephan %A Hammer, Peter L. %A Hellerstein, Lisa %T Equational Theories of Boolean Functions %D December 10, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-79 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-70.ps.gz %X Several noteworthy classes of Boolean functions are characterized by algebraic identities. For a given DNF-specified class, such characteristic identities exist if and only if the class is closed under the operation of forming Boolean minors by variable identification. A single identity suffices to characterize a class if and only if the number of forbidden identification minors minimal in a specified sense is finite. If general first-order sentences are allowed instead of identities only, then essentially all classes can be described by an appropriate set of sentences. %A Feigenbaum, Joan %T DIMACS Research and Education Institute (DREI '97) Cryptography and Network Security (July 28 - August 15, 1997) Abstracts of Talks Presented %D December 12, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-80 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-70.ps.gz %X During the summer of 1997 we held a three-week program of research workshops aimed at scientists from academia and industry, and open to graduate students and postdoctoral fellows, along with an educational program for high school and college teachers, undergraduates and others. In addition, there were plenary sessions and evening lectures aimed at meshing the two groups in discussion and problem-solving and creating partnerships in the educational enterprise. %A Beimel, Amos %A Gal, Anna %T On Arithmetic Branching Programs %D December 12, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-81 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-70.ps.gz %X We consider the model of arithmetic branching programs, which is a generalization of modular branching programs. We show that, up to a polynomial factor in size, arithmetic branching programs are equivalent to complements of dependency programs, a model introduced by Pudlak and Sgall in 1996. Using this equivalence we prove that dependency programs are closed under conjunction, answering an open problem of Pudlak and Sgall. Furthermore, we show that span programs, an algebraic model of computation introduced by Karchmer and Wigderson in 1993, are at least as strong as arithmetic programs; every arithmetic program can be simulated by a span program of size not more than twice the size of the arithmetic program. Using the above results we give a new proof that the class NL/poly is contained in the class parity-L/poly, first proved by Wigderson in 1994. Our simulation of NL/poly is more efficient, and it holds for logspace counting classes over every field. %A Boros, Endre %A Unluyurt, Tonguc %T Diagnosing Double Regular Systems %D December 16, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-82 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-70.ps.gz %X We consider the problem of testing sequentially the components of a double regular system, when the testing of each component is costly. Generalizing earlier results about $k$-out-of-$n$ systems, we provide a polynomial time algorithm for the most cost-effficient sequential testing of double regular systems. The algorithm can be implemented to work efficiently both for explicitly given systems, and for systems given by an oracle. %A Landweber, Laura F. %T RNA Based Computing %D December 20, 1997 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 97-83 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-70.ps.gz %X

This report will focus on a combined treatment of the fields of RNA evolution and DNA computers. Using examples of in vitro selection of functional RNA molecules from large pools of random sequences, I show that these experiments can be viewed as an "RNA computer", in the language of DNA computation. By applying a strict set of criteria to a pool of heterogeneous DNA or RNA sequences, both types of experiments find sequences that contain solutions to hard molecular computational problems. These can even be nondigital problems that an electronic computer cannot solve. For example, a problem I addressed using a pool of RNA molecules was one of catalysis, or the ability to ligate a small substrate RNA molecule to itself. In vitro evolution searches for the best solution or class of solutions contained within a large library of approximately 10^15 unique sequences. The advantage of these "molecular computers" is their ability to examine and eliminate billions of possible solutions in parallel. We also describe an example of a cellular paradigm for RNA-based computing: RNA editing.

From the Second Annual DIMACS Meeting on DNA Based Computers, June 10-12, 1996 and the DIMACS Special Focus on DNA Computing. %A Belegradek, Oleg V. %A Stolboushkin, Alexei P. %A Taitslin, Michael A. %T On Order-Generic Queries %D January 31, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %R 96-01 %X We consider relational databases organized over an ordered domain with some additional relations---a typical example is the ordered domain of rational numbers together with the ternary relation $+$ of addition. In the focus of our study are the first order queries that are invariant under order-preserving ``permutations''---such queries are called order-generic. In fact, we consider two formalizations of this notion: ``generic'', and ``locally generic'', queries. For several domains order-generic queries fail to express more than pure order queries, for example, every order-generic query over rational numbers with $+$ can be rewritten without $+$. Our goal is to find general conditions on the domain that allow for such a simplification of order-generic queries. An important difference of this paper from a recent series of related papers (see, for example,~\cite{PBG95,BDLW95}) is that we generalize all notions to the case of finitely representable database states---as opposed to finite states---and develop a general lifting technique that, essentially, allows us to extend any result of the kind we are interested in, from finite to finitely-representable states, and thus all the results in this paper are proved for the general case of {\em constraint databases.} On the simplification of order-generic queries, we offer two types of results. The results of the first type address {\em equivalence\/} of order-generic queries that use the additional predicates (extended queries) to pure order queries. Here we establish the necessary and sufficient condition for an extended query to be equivalent to a pure order query, in terms of behavior of this extended query over the ultra-product of this domain by a non-principal ultra-filter over $\omega$. This characterization relies upon the Continuum Hypothesis, and is used as instrumental in establishing equivalence of generic, as well as locally generic, extended queries to pure order queries for several classes of domains, including in particular the so-called $o$-minimal domains, integers with $+$, and such. Although, by Shoenfield's Absoluteness Theorem, the Continuum Hypothesis can be eliminated from these latter results, the fact remains, no translation algorithm can be extracted from arguments of this type. That is why we also offer {\em effective algorithms\/} of translating extended to pure order queries for divisible ordered Abelian groups. Such groups---including real or rational numbers with $+$---are all $o$-minimal. %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-01.ps.gz %A Blaze, Matt %A Feigenbaum, Joan %A Leighton, F. T. %T Master-Key Cryptosystems %D February 4, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %R 96-02 %I DIMACS %X We initiate the study of a new class of secret-key cryptosystems, called "master-key cryptosystems," in which an authorized third party possesses a "master key" that allows efficient recovery of the cleartext without knowledge of the session key. One motivation for this study is that master-key cryptosystems could provide a less cumbersome alternative to "key escrow" in situations in which third-party access is required. We demonstrate that designing a master-key cryptosystem with acceptable performance is roughly equivalent to designing a public-key cryptosystem in which encryption is much faster than is possible with current public-key techniques. %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-02.ps.gz %A Allender, Eric %A Jiao, Jia %A Mahajan, Meena %A Vinay, V. %T Non-Commutative Arithmetic Circuits: Depth Reduction and Size Lower Bounds %D February 7, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %R 96-03 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-03.ps.gz %X We investigate the phenomenon of depth-reduction in commutative and non-commutative arithmetic circuits. We prove that in the commutative setting, uniform semi-unbounded arithmetic circuits of logarithmic depth are as powerful as uniform arithmetic circuits of polynomial degree; earlier proofs did not work in the uniform setting. This also provides a unified proof of the circuit characterizations of LOGCFL and #LOGCFL. We show that AC^1 has no more power than arithmetic circuits of polynomial size and degree n^{O(log log n)} (improving the trivial bound of n^{O(log n)}). Connections are drawn between TC^1 and arithmetic circuits of polynomial size and degree. Then we consider non-commutative computation, and show that some depth reduction is possible over the algebra (Sigma^*, max, concat), thus establishing that OptLOGCFL is in AC^1. This is the first depth-reduction result for arithmetic circuits over a noncommutative semiring, and it complements the lower bounds of Kosaraju and Nisan showing that depth reduction cannot be done in the general noncommutative setting. We define new notions called ``short-left-paths'' and ``short-right-paths'' and we show that these notions provide a characterization of the classes of arithmetic circuits for which optimal depth-reduction is possible. This class also can be characterized using the AuxPDA model. Finally, we characterize the languages generated by efficient circuits over the (union, concat) semiring in terms of simple one-way machines, and we investigate and extend earlier lower bounds on non-commutative circuits. %A Agrawal, Manindra %A Allender, Eric %T An Isomorphism Theorem for Circuit Complexity %D February 26, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %R 96-04 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-04.ps.gz %X We show that all sets complete for NC^1 under AC^0 reductions are isomorphic under AC^0-computable isomorphisms. Although our proof does not generalize directly to other complexity classes, we do show that, for all complexity classes C closed under NC^1-computable many-one reductions, the sets complete for C under NC^0 reductions are all isomorphic under AC^0-computable isomorphisms. Our result showing that the complete degree for NC^1 collapses to an isomorphism type follows from a theorem showing that in NC^1, the complete degrees for AC^0 and NC^0 reducibility coincide. This theorem does not hold for strongly uniform reductions: we show that there are Dlogtime-uniform AC^0-complete sets for NC^1 that are not Dlogtime-uniform NC^0-complete. %A Bisztriczky, Tibor %A Karolyi, Gyula %T Subpolytopes of Cyclic Polytopes %D February 26, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %R 96-05 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-05.ps.gz %X A remarkable result of I. Shemer [4] states that the combinatorial structure of a neighbourly $2m$-polytope determines the combinatorial structure of each of its subpolytopes. From this, it follows that every subpolytope of a cyclic $2m$-polytope is cyclic. In this note, we present a direct proof of this consequence that also yields that certain subpolytopes of a cyclic $(2m+1)$-polytope are cyclic. %A Kaplan, Haim %A Tarjan, Robert E. %T Purely Functional Representations of Catenable Sorted Lists %D February 8, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %R 96-06 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-06.ps.gz %X The power of purely functional programming in the construction of data structures has received much attention, not only because functional languages have many desirable properties, but because structures built purely functionally are automatically {\em fully persistent}: any and all versions of a structure can coexist indefinitely. Recent results illustrate the surprising power of pure functionality. One such result was the development of a representation of double-ended queues with catenation that supports all operations, including catenation, in worst-case constant time~\cite{KaTar}. This paper is a continuation of our study of pure functionality, especially as it relates to persistence. For one purposes, a purely functional data structure is one built only with the LISP functions car, cons, cdr. We explore purely functional representations of sorted lists, implemented as finger search trees. We describe three implementations. The most efficient of these achieves logarithmic access, insertion, and deletion time, and double-logarithmic catenation time. It uses one level of structural bootstrapping to obtain its efficiency. The bounds for find, insert, and delete are the same as the best known bounds for an ephemeral implementation of these operations using finger search trees. The representations we present are the first that address the issues of persistence and pure functionality, and the first for which fast implementations of catenation and split are presented. They are simple to implement and could be efficient in practice, especially for applications that require worst-case time bounds or persistence. %A Karolyi, Gyula %A Pach, Janos %A Tardos, Gabor %A Toth, Geza %T An algorithm for finding many disjoint monochromatic edges in a complete 2-colored geometric graph %D April 9, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %R 96-07 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-07.ps.gz %X We present an $O(n^{\log\log n+2})$-time algorithm for finding $n$ disjoint monochromatic edges in a complete geometric graph of $3n-1$ vertices, where the edges are colored by two colors. %A Sazonov, Vladimir Yu %A Sviridenko, Dmitri I. %T Abstract Deducibility and Domain Theory %D April 9, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %R 96-08 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-08.ps.gz %X According to the thesis ``computability = deducibility'' [D.Scott, LNCS 140] there are investigated intensional aspects of domain theory as mathematical theory of computability.

A logistic system is any pair of sets , where R \subseteq Conf(A) := Powerset(A) x (A union {#}), # \notin A. The intended interpretation: A is a set of sentences, R is a rule of inference, and # is a contradiction sign. As usually, R induces a relation |-_R \subseteq Conf(A) of (reflexive) deductive inference and also the classes Cl() \subseteq Powerset(A) of the closed sets under |-_R and Th() \subseteq Cl() of consistent closed sets (theories) partially ordered by the inclusion relation. The followimg more general notion of deducibility ||-_R, which may be non-reflexive, playes an important role. Let G ||-_R f iff there exists a (well-founded) tree of inference G ||-_R f which contains at least one configuration in R (i.e. is non-trivial). By imposing, if necessary, on deducibility notion suitable finitarity conditions (and others) it is possible to characterise rather naturally, from the point of view of the abovementioned thesis, various classes of domains, e.g. classes of all complete lattices with a base, conditionally complete partially ordered sets with a base, complete f_0-spaces (defined in [Ju.L.Ershov, Algebra and Logic, 11, N4], the same as Scott's algebraic domains; cf. also [D.Scott, LNCS 140] where only finitary reflexive deducibility is considered), Ershov's complete A_0-spaces [Algebra and Logic, 12, N4] = Scott's continuous domains, and Scott's continuous lattices. For example, Th(< A,|- >) is an (arbitrary) complete A_0-space under \subseteq if for some R \subseteq Conf(A) there holds

(1) G/f \in R => G is finite, (i.e. R is finitary), (2) G ||-_R f => G^ ||-_R f, where G^ := union {g^ : g \in G and g^ := {h : g ||-_R h}, and (3) G |- f <=> G ||-_R f^ and $G |- # <=> G ||-_R #.

The goal of this paper is just to give an English extended version of the above text published only in Russian [V.Yu.Sazonov and D.I.Sviridenko, Abstract Deducibility and Domain Theory, Seventh All Union Conference on Mathematical Logic, Abstracts, Novosibitsk, 1984, p. 158] in connection with a related recent paper [R.Hoofman, Continuous Information Systems, Information and Computation 105, 42--71 (1993)]. It contains also an Appendix to this Abstract (written by the first author) with additional details, proofs and some comparisons with Hoofman's approach. %A Gibbons, Luana E. %A Hearn, Donald W. %A Pardalos, Panos M. %A Ramana, Motakuri V. %T Continuous Characterizations of the Maximum Clique Problem %D April 9, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %R 96-09 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-09.ps.gz %X Given a graph $G$ whose adjacency matrix is $A$, the Motzkin-Strauss formulation of the Maximum-Clique Problem is the quadratic program $\max\{x^TAx|x^Te=1,x\geq 0\}$. It is well known that the global optimum value of this QP is $(1-1/\omega(G))$, where $\omega(G)$ is the clique number of $G$. Here, we characterize the following: 1) first order optimality 2) second order optimality 3) local optimality 4) strict local. These characterizations reveal interesting underlying discrete structures, and are polynomial time verifiable. A parametrization of the Motzkin-Strauss QP is then introduced and its properties are investigated. Finally, an extension of the Motzkin-Strauss formulation is provided for the weighted clique number of a graph and this is used to derive a maximin characterization of perfect graphs. %A Komlos, Janos %A Simonovits, Miklos %T Szemeredi's Regularity Lemma and its applications in graph theory %D April 7, 1995 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-10 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-10.ps.gz %X Szemer\'edi's Regularity Lemma is an important tool in discrete mathematics. It says that, in some sense, all graphs can be approximated by random-looking graphs. Therefore the lemma helps in proving theorems for arbitrary graphs whenever the corresponding result is easy for random graphs. Recently quite a few new results were obtained by using the Regularity Lemma, and also some new variants and generalizations appeared. In this survey we describe some typical applications and some generalizations. %A Cherlin, Gregory L. %A Latka, Brenda J. %T A Decision Problem Involving Tournaments %D May 13, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-11.ps.gz %R 96-11 %X A class of finite tournaments determined by a set of ``forbidden subtournaments'' is well-quasi-ordered if and only if it contains no infinite antichain (a set of incomparable elements). It is not known if there is an algorithm which decides whether or not a class of finite tournaments determined by a finite set of forbidden subtournaments has this property. We prove a noneffective finiteness theorem bearing on the problem. We show that for each fixed $k$, there is a finite set of infinite antichains, $\Lambda_k$, with the following property: if any class defined by $k$ forbidden subtournaments contains an infinite antichain, then a cofinite subset of an element of $\Lambda_k$ must be such an antichain. By refining this analysis and using an earlier result giving an explicit algorithm for the case $k=1$, we show that there exists an algorithm which decides whether or not a class of finite tournaments determined by two forbidden subtournaments is well-quasi-ordered.

footnote:

This work was the result of the authors' collaboration during the 95/96 Special Year on Logic and Algorithms. %A Trenk, Ann N. %T k-Weak Orders: Recognition and a Tolerance Result %D June 24, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %R 96-12 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-12.ps.gz %X In this paper we introduce a family of ordered sets we call {\em k-weak orders\/} which generalize weak orders, semi-orders, and bipartite orders. For each $k$, we give a polynomial-time recognition algorithm for $k$-weak orders and a partial characterization. In addition, we prove that among 1-weak orders, the classes of bounded bitolerance orders and totally bounded bitolerance orders are equal. This enables us to recognize the class of totally bounded bitolerance orders for 1-weak orders. %A Annexstein, Fred %A Berman, Ken %A Swaminathan, Ram %T Independent Spanning Trees with Small Stretch Factors %D June 28, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-13 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-13.ps.gz %X A pair of spanning trees rooted at a vertex "r" are independent if for every vertex "v" the pair of unique tree paths from "v" to the root "r" are disjoint. This paper presents the first analysis of the path lengths involved in independent spanning trees in 2-edge-connected and 2-vertex-connected graphs. We present upper and lower bounds on the stretch factors of pairs of independent spanning trees, where the stretch factor of a spanning tree is defined to be the maximum ratio between the length of paths in the tree to the root to the length of the shortest path in the graph to the root. We prove that if "G" is a 2-edge-connected graph with the property that every edge lies on a cycle of size at most "h", then we can construct in linear time a pair of edge-independent spanning trees whose stretch factors are bounded by O(h). In fact, we prove a more general result, namely that the stretch factor of both independent trees can be bounded by a minimax length of ears with respect to a certain class of ear decompositions of the graph. We demonstrate analogous constructions of vertex-independent spanning trees with bounded stretch factors for the class of 2-vertex-connected graphs. We show that our upper bounds are existentially optimal, that is, there are classes of graphs for which our bounds are tight. --------------------------------------- The last author would like to acknowledge the hospitality of DIMACS Center. %A Thorup, Mikkel %T Sorting in O(n log log n) time and linear space using addition, shift, and bit-wise boolean operatations %D June 28, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %R 96-14 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-14.ps.gz %X We present a randomized sorting algorithm doing as described in the title. %A Brayton, R. %A Emerson, A. %A Feigenbaum, J. %T Workshop Summary: Computational and Complexity Issues in Automated Verification %D June 28, 1996 %Z Mon, 2 Dec 1996 15:27:22 GMT %R 96-15 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-15.ps.gz %X The correctness of computer hardware and software is an area of growing theoretical interest and practical importance. It is now widely acknowledged that effective reasoning about program correctness requires: (i) the use of appropriate formalisms, such as temporal logic or automata, for rigorously specifying correct behavior, and (ii) the use of mechanical reasoning algorithms, such as model checkers, to permit proofs of correctness to be constructed automatically that could not reasonably be constructed by hand owing to the intractable amount of tedious detail. A principal limiting factor in automated verification is the computational complexity of various associated mechanical reasoning problems; this complexity might be prohibitively high because of the combinatorial state explosion problem, which appears in many guises.

The DIMACS Workshop on Computational and Complexity Issues in Automated Verification, held at Rutgers University on March 25-28, 1996, and organized by Bob Brayton (University of California at Berkeley), Allen Emerson (University of Texas), Joan Feigenbaum (AT&T Research), featured both theoretical and practical work in this important area of computer science. This report contains short abstracts of all talks given at the workshop, as well as pointers to sources of more information. %A Feigenbaum, Joan %A Fortnow, Lance %A Laplante, Sophie %A Naik, Ashish %T On Coherence, Random-Self-Reducibility, and Self-Correction %D June 28, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %R 96-16 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-16.ps.gz %X We address two questions about self-reducibility -- the power of adaptiveness in examiners that take advice and the relationship between random-self-reducibility and self-correctability. We first show that adaptive examiners are more powerful than nonadaptive examiners, even if the nonadaptive ones are nonuniform. Blum et al. [Blum, Luby and Rubinfeld, Journal of Computer and System Sciences, 59:549--595, 1993] showed that every random-self-reducible function is self-correctable. However, whether self-correctability implies random-self-reducibility is unknown. We show that, under a reasonable complexity hypothesis, there exists a self-correctable function that is not random-self-reducible. For P-sampleable distributions, however, we show that constructing a self-correctable function that is not random-self-reducible is as hard as proving that P is not equal to PP.

This work was presented in preliminary form at the IEEE Conference on Computational Complexity, Philadelphia PA, May 1996. %A Blaze, Matt %A Feigenbaum, Joan %A Lacy, Jack %T Decentralized Trust Management %D June 28, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %R 96-17 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-17.ps.gz %X We identify the "trust management problem" as a distinct and important component of security in network services. Aspects of the trust management problem include formulating security policies and security credentials, determining whether particular sets of credentials satisfy the relevant policies, and deferring trust to third parties. Existing systems that support security in networked applications, including X.509 and PGP, address only narrow subsets of the overall trust management problem and often do so in a manner that is appropriate to only one application. We present a comprehensive approach to trust management, based on a simple language for specifying trusted actions and trust relationships. We also describe a prototype implementation of a "trust management system," called PolicyMaker, that can facilitate the development of security features in a wide range of network services.

This paper was presented at the IEEE Symposium on Security and Privacy, Oakland CA, May 1996. %A Porkolab, Lorant %A Khachiyan, Leonid %T On the Complexity of Semidefinite Programs %D June 28, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %R 96-18 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-18r.ps.gz %X We show that the feasibility of a system of $m$ linear inequalities over the cone of symmetric positive semidefinite matrices of order $n$ can be tested in $mn^{O(\min\{m,n^2\})}$ arithmetic operations over $ln^{O(\min\{m,n^2\})}$-bit numbers, where $l$ is the maximum binary size of the input coefficients. We also show that any feasible system of dimension $(n,m)$ has a solution $\M{X}$ such that $\log \|\M{X}\| \le ln^{O(\min\{m,n^2\})}$. %A Steel, Mike %A Szekely, Laszlo A. %A Erdos, Peter L. %T The number of nucleotide sites needed to accurately reconstruct large evolutionary trees %D June 28, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %R 96-19 %I DIMACS %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-19.ps.gz %X Biologists seek to reconstruct evolutionary trees for increasing number of species, $n$, from aligned genetic sequences. How fast the sequence length $N$ must grow, as a function of $n$, in order to accurately recover the underlying tree with probability $1-\epsilon$, if the sequences evolve according to simple stochastic models of nucleotide substitution? We show that for a certain model, a reconstruction method exists for which the sequence length $N$ can grow surprisingly slowly with $n$ (sublinearly for a wide range of parameters, and even as a power of $\log n$ in a narrow range, which roughly meets the lower bound from information theory). By contrast a more traditional technique (maximum compatibility) provably requires $N$ to grow faster than linearly in $n$. Our approach is based on a new, and computationally efficient approach for reconstructing phylogenetic trees from aligned DNA sequences. %A Kayll, P. Mark %T Asymptotics of the total chromatic number for simple graphs %D July 2, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-20 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-20.ps.gz %X For simple graphs, the ratio of the total chromatic number to its linear analogue, the fractional total chromatic number, tends to one as the latter parameter grows large. Two short proofs of this fact, first observed here, are presented. One is based on a theorem of Kahn ({\em J.\ Combin.\ Theory Ser.\ A} {\bf 73} (1996), 1--59) concerning the asymptotics of the list-chromatic index, the other on recent progress of Molloy and Reed in the direction of the ``Behzad-Vizing Conjecture''. The main result has the flavour of several recent others establishing asymptotic agreement of certain integral (hyper)graph parameters with their fractional analogues. %A Kupferman, Orna %A Vardi, Moshe Y. %T Verification of Fair Transition Systems %D July 8, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-21 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-21.ps.gz %X In {\em program verification\/}, we check that an {\em implementation\/} meets its {\em specification}. Both the specification and the implementation describe the possible behaviors of the program, though at different levels of abstraction. We distinguish between two approaches to implementation of specifications. The first approach is {\em trace-based implementation}, where we require every computation of the implementation to correlate to some computation of the specification. The second approach is {\em tree-based implementation}, where we require every computation tree embodied in the implementation to correlate to some computation tree embodied in the specification. The two approaches to implementation are strongly related to the linear-time versus branching-time dichotomy in temporal logic.

In this work we examine the trace-based and the tree-based approaches from a {\em complexity-theoretic\/} point of view. We consider and compare the complexity of verification of {\em fair transition systems}, modeling both the implementation and the specification, in the two approaches. We consider {\em unconditional, weak\/}, and {\em strong\/} fairness. For the trace-based approach, the corresponding problem is {\em fair containment}. For the tree-based approach, the corresponding problem is {\em fair simulation}. We show that while both problems are PSPACE-complete, their complexities in terms of the size of the implementation do not coincide and the trace-based approach is easier. As the implementation is normally much bigger than the specification, we see this as an advantage of the trace-based approach. Our results are at variance with the known results for the case of transition systems with no fairness, where no approach is evidently advantageous. %A Boerger, E. %A Mazzanti, S. %T A Correctness Proof for Pipelining in RISC Architecture %D July 8, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-22 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-22.ps.gz %X We describe a technique for specifying and verifying the control of pipelined microprocessors which can be used where traditional or purely automatic methods do not scale up to complex commercial microprocessor design. We illustrate our approach through a formal specification of Hennessy's and Patterson's RISC processor DLX for which we prove the correctness of its pipelined model with respect to the sequential model.

First we concentrate our attention on the provably correct refinement of the sequential ground model DLX to the pipelined parallel version DLX_p in which structural hazards (resource conflicts) are eliminated. Then we extend the result to the model DLX_data in which also data hazards for not jump instructions are treated. The next step consists of building the model DLX_control in which control hazards are eliminated. In the last step we define DLX_pipe and prove that it refines DLX_control correctly and takes care also of data hazards relative to jump instructions.

Due to the systematic use of successive refinements, which are organized around the different pipelining problems and the methods for their solution, our approach can be applied for the design-driven verification as well as for the verification-driven design of RISC cores at any level of abstraction. The proof method supports the designer's intuitive reasoning; ``local'' argumentations, which are typical for incremental design and for optimizations, are supported by the semantical modularity of the design and proof method. The specification method supports the descriptive part of the designer's actual work; it is general and can be applied to other microprocessors and pipelining techniques as well. Since our models come in the form of evolving algebras, they can be made executable by evolving algebra interpreters and can thereby be used for (prototypical) simulations.

NOTE: The first author wants to express his thanks to $DIMACS$ for the hospitality during the Fall of 1995 when part of this work was done. %A Bloch, Stephen %T Integer NC^1 is equal to Boolean NC^1 %D July 8, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-23 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-23.ps.gz %X We show that the product of $n$ $3 \times 3$ matrices of $n$-bit integers can be computed in $P$-uniform $FNC^1$. Since this problem is complete~\cite{BOC:const_registers} for formul\ae\ in $\{+, \cdot\}$ on $n$-bit integers, we conclude that ``algebraic $NC^1$'' on integers is equal to the usual Boolean notion of $NC^1$ functions. %A Koiran, Pascal %T Elimination of Constants from Machines over Algebraically Closed Fields %D July 8, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-24 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-24.ps.gz %X Let $\k$ be an algebraically closed field of characteristic 0. We show that constants can be removed efficiently from any machine over $\k$ solving a problem which is definable without constants. This gives a new proof of the transfer theorem of Blum, Cucker, Shub \& Smale for the problem $\p \stackrel{?}{=}\np$. We have similar results in positive characteristic for non-uniform complexity classes. We also construct explicit and correct test sequences (in the sense of Heintz and Schnorr) for the class of polynomials which are easy to compute.

An earlier version of this paper appeared as NeuroCOLT Technical Report 96-43. The present paper contains in particular a new bound for the size of explicit correct test sequences. %A Koiran, Pascal %A Moore, Cristopher %T Closed-form Analytic Maps in One and Two Dimensions Can Simulate Turing Machines %D July 15, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-25 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-25.ps.gz %X We show closed-form analytic functions consisting of a finite number of trigonometric terms can simulate Turing machines, with exponential slowdown in one dimension or in real time in two or more. %A Saks, Michael %A Srinivasan, Aravind %A Zhou, Shiyu %T Explicit OR-Dispersers with Polylogarithmic Degree %D July 30, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-26 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-26.ps.gz %X An $(N,M,T)$-OR-disperser is a bipartite multigraph $G=(V,W,E)$ with $|V|=N$, and $|W|=M$, having the following expansion property: any subset of $V$ having at least $T$ vertices has a neighbor set of size at least $M/2$. For any pair of constants $\xi,\lam, 1\ge\xi>\lam\ge 0$, any sufficiently large $N$, and for any $T\ge 2^{(\log N)^{\xi}}$, $M \leq 2^{(\log N)^{\lam}}$, we give an explicit elementary construction of an $(N,M,T)$-OR-disperser such that the out-degree of any vertex in $V$ is at most polylogarithmic in $N$. Using this with known applications of OR-dispersers yields several results. First, our construction implies that the complexity class Strong-RP defined by Sipser, equals RP. Second, for any fixed $\eta > 0$, we give the first polynomial-time simulation of RP algorithms using the output of any ``$\eta$-minimally random'' source. For any integral $R > 0$, such a source accepts a single request for an $R$-bit string and generates the string according to a distribution that assigns probability at most $2^{-R^\eta}$ to any string. It is minimally random in the sense that any weaker source is insufficient to do a black-box polynomial-time simulation of RP algorithms. %A Koiran, Pascal %T Hilbert's Nullstellensatz is in the Polynomial Hierarchy %D July 30, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-27 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-27.ps.gz %X We show that if the Generalized Riemann Hypothesis is true, the problem of deciding whether a system of polynomial equations in several complex variables has a solution is in the second level of the polynomial hierarchy. In fact, this problem is in AM, the ``Arthur-Merlin'' class (recall that $\np \subseteq \am \subseteq \rp^{\tiny \np} \subseteq \Pi_2$). The best previous bound was PSPACE.

An earlier version of this paper was distributed as NeuroCOLT Technical Report~96-44. The present paper includes in particular a new lower bound for unsatisfiable systems, and remarks on the Arthur-Merlin class. %A Therien, Denis %A Wilke, Thomas %T Temporal Logic and Semidirect Products: An Effective Characterization of the Until Hierarchy %D July 30, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-28 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-28.ps.gz %X We reveal an intimate connection between semidirect products of finite semigroups and substitution of formulas in linear temporal logic. We use this connection to obtain an algebraic characterization of the `until' hierarchy of linear temporal logic; the k-th level of that hierarchy is comprised of all temporal properties that are expressible by a formula of nesting depth k in the `until' operator. Applying deep results from finite semigroup theory we are able to prove that each level of the `until' hierarchy is decidable. %A Bafna, Vineet %A Berman, Piotr %A Fujito, Toshihiro %T Constant Ratio Approximations of Feedback Vertex Sets in Weighted Undirected Graphs %D July 30, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-29 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-29.ps.gz %X A feedback vertex set of a graph is a subset of vertices that contains at least one vertex from every cycle in the graph. We show that a feedback vertex set approximating a minimum one within a constant factor can be efficiently found in undirected graphs. In fact the derived approximation ratio matches the best constant ratio known today for the vertex cover problem, improving the previous best results for both weighted and unweighted cases. The existence of an approximation preserving reduction of the vertex cover problem to the feedback vertex set problem suggests that further improvement of the obtained ratio will require entirely new ideas.

We extend our approach to handle graphs of bounded vertex degree, and show an improved performance ratio for this case. These approximation bounds are obtained by using a non--trivial generalization of the classical local ratio principle of Bar--Yehuda and Even. %A Bafna, V. %A Muthukrishnan, S. %A Ravi, R. %T Computing similarity between RNA strings %D July 30, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-30 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-30.ps.gz %X Ribonucleic acid (RNA) strings are strings over the four-letter alphabet {A,C,G,U} with a secondary structure of base-pairing between A-U and C-G pairs in the string. Edges are drawn between two bases that are paired in the secondary structure and these edges have traditionally been assumed to be noncrossing. The noncrossing base-pairing naturally leads to a tree-like representation of the secondary structure of RNA strings.

In this paper, we address several notions of similarity between two RNA strings that take into account both the primary sequence and secondary base-pairing structure of the strings. We present efficient algorithms for exact matching and approximate matching between two RNA strings. We define a notion of alignment between two RNA strings and devise algorithms based on dynamic programming. We then present a method for optimally aligning a given RNA sequence with unknown secondary structure to one with known sequence and structure, thus attacking the structure prediction problem in the case when the structure of a closely related sequence is known. The techniques employed to prove our results include reductions to well-known string matching problems, allowing wild cards and ranges, and speeding up dynamic programming by using the tree structures implicit in the secondary structure of RNA strings. %A Kelmans, Alexander K. %T Packing of induced stars in a graph %D July 31, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-31 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-31.ps.gz %X We consider simple undirected graphs. An edge subset $A$ of $G$ is called an {\em induced $n$--star packing} of $G$ if every component of the subgraph $G[A]$ induced by $A$ is a star with at most $n$ edges and is an induced subgraph of $G$. We consider the problem of finding an induced $n$--star packing of $G$ that covers the maximum number of vertices. This problem is a natural generalization of the classical matching problem. We show that many classical results on matchings (such as the Tutte 1-Factor Theorem, the Berge Duality Theorem, the Gallai--Edmonds Structure Theorem, the Matching Matroid Theorem) can be extended to induced $n$--star packings in a graph. %A Apartsin, A. %A Ferapontova, E. %A Gurvich, V. %T A Circular Graph - Counterexample to the Duchet Kernel Conjecture %D August 5, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-32 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-32.ps.gz %X We construct a directed graph G such that a) G is strongly connected, b) G has the circular symmetry, c) G is not a directed odd cycle, d) G has no kernel but e) after removing any edge from G the obtained graph has a kernel . %A Boros, E. %A Gurvich, V. %A Vasin, A. %T Stable Families of Coalitions and Normal Hypergraphs %D August 5, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-33 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-33.ps.gz %X The core of a game is defined as the set of outcomes acceptable for {\em all} coalitions. This is probably the simplest and most natural concept of cooperative game theory. However, the core can be empty because there are too many coalitions. Yet, some players may not like or know each other, so they cannot form a coalition. Let $\cK$ be a fixed family of coalitions. The $\cK$-core is defined as the set of outcomes acceptable for all the coalitions from $\cK$. The family $\cK$ is called {\em stable} if the $\cK$-core is not empty for any normal form game (or equivalently, for any game in generalized characteristic function form). \\*[\parskip] \hspace*{1.5em}{\em Normal hypergraphs} can be characterized by several equivalent properties, e.g. they are {\em dual} to the {\em clique hypergraphs} of {\em perfect graphs}. We prove that a family $\cK$ of coalitions is stable iff $\cK$ as a hypergraph is normal. %A Boros, E. %A Gurvich, V. %T Stable Effectivity Functions and Perfect Graphs %D August 5, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-34 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-34.ps.gz %X An effectivity function $\cE$ is called {\em stable} if the core $C(\cE,u)$ is not empty for any payoff $u$. The problem to characterize stable effectivity functions seems, in general, very difficult. In this paper we apply a graph theoretic approach to this problem. Using a graph based model we obtain some necessary and some sufficient conditions for stability in terms of perfect graphs. We also demonstrate that the conjecture by Berge and Duchet (1983) related to perfect graphs and kernels, in fact, is a special case of the considered problem of stability of effectivity functions. %A Gurvich, Vladimir %T Dual Graphs on Surfaces %D August 5, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-35 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-35.ps.gz %X Consider an embedding of a graph $G$ in a surface $S$ ({\it map}). Assume that the difference splits into connected components ({\it countries}), each one homeomorphic to an open disk. (It follows from this assumption that graph $G$ must be connected). Introduce a graph $G^*$ dual to $G$ realizing the neighbor relations among countries. The graphs $G$ and $G^*$ have the same set of edges. More precisely, there is a natural one-to-one correspondence between their edge-sets. An arbitrary pair of graphs with common set of edges is called a {\it plan}. Every map induces a plan. A plan is called {\it \bf geographic} if it is induced by a map. In terms of Eulerian graphs we obtain criteria for a plan to be geographic. We also give an algorithm of reconstruction a map from a geographic plan. A case when this map is unique is singled out. Partially, these results were announced by Gurvich and Shabat in 1989. %A Coffman, E. G., Jr. %A Kahale, Nabil %A Leighton, F. T. %T Processor-Ring Communication: A Tight Asymptotic Bound on Packet Waiting Times %D August 14, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-36 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-36.ps.gz %X We consider $N$ processors communicating unidirectionally over a closed transmission channel, or ring. Each message is assembled into a fixed-length packet. Packets to be sent are generated at random times by the processors, and the transit times spent by packets on the ring are also random. Packets being forwarded, i.e., packets already on the ring, have priority over waiting packets. The objective of this paper is to analyze packet waiting times under a greedy policy, within a discrete Markov model that retains the over-all structure of a practical system, but is simple enough so that explicit results can be proved. Independent, identical Bernoulli processes model message generation at the processors, and i.i.d. geometric random variables model the transit times. Our emphasis is on asymptotic behavior for large ring sizes, $N$, when the respective rate parameters have the scaling $\la /N$ and $\mu /N$. Our main result shows that, if the traffic intensity is fixed at $\rho = \la / \mu < 1$, then as $N \to \infty$ the expected time a message waits to be put on the ring is bounded by a constant. This result verifies that the expected waiting time under the greedy policy is within a constant factor of that under an optimal policy. %A Babai, Laszlo %A Gal, Anna %A Wigderson, Avi %T Superpolynomial Lower Bounds for Monotone Span Programs %D September 8, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-37 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-37.ps.gz %X In this paper we obtain the first superpolynomial lower bounds for {\it monotone span programs} computing explicit functions. The best previous lower bound was $\Omega(n^{5/2})$ by Beimel, G\'al, Paterson \cite{BGP}; our proof exploits a general combinatorial lower bound criterion from that paper. Our lower bounds are based on an analysis of Paley-type bipartite graphs via Weil's character sum estimates. We prove an $n^{\Omega ( \log n / \log\log n)}$ lower bound for an explicit family of monotone Boolean functions in $n$ variables, which implies the same lower bound for the size of monotone span programs for the clique problem. Our results give the first superpolynomial lower bounds for linear secret sharing schemes.

We demonstrate the surprising power of monotone span programs by exhibiting a function computable in this model in linear size while requiring superpolynomial size monotone circuits and exponential size monotone formulae. We also show that the perfect matching function can be computed by polynomial size (non-monotone) span programs over arbitrary fields. %A Ouyang, Ming %T How good are branching rules in DPLL? %D September 9, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-38 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-38.ps.gz %X The Davis-Putnam-Logemann-Loveland algorithm is one of the most popular algorithms for solving the satisfiability problem. Its efficiency depends on its choice of a branching rule. We construct a sequence of instances of the satisfiability problem that fools a variety of ``sensible'' branching rules in the following sense: when the instance has n variables, each of the ``sensible'' branching rules brings about Omega(2^(n/5)) recursive calls of the Davis-Putnam-Logemann-Loveland algorithm, even though only O(1) such calls are necessary. %A van Melkebeek, Dieter %T Deterministic and Randomized Bounded Truth-table Reductions of P, NL, and L to Sparse Sets %D September 11, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-39 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-39.ps.gz %X We prove that there is no sparse hard set for P under logspace computable bounded truth-table reductions unless P = L. In case of reductions computable in NC1, the collapse goes down to P = NC1.

We parameterize this result and obtain a generic theorem allowing to vary the sparseness condition, the space bound and the number of queries of the truth-table reduction. Another instantiation yields that there is no quasipolynomially dense hard set for P under polylog-space computable truth-table reductions using polylogarithmically many queries unless P is in polylog-space.

We also apply the proof technique to NL and L. We establish that there is no sparse hard set for NL under logspace computable bounded truth-table reductions unless NL = L, and that there is no sparse hard set for L under NC1-computable bounded truth-table reductions unless L = NC1.

We show that all these results carry over to the randomized setting: If we allow two-sided error randomized reductions with confidence at least inversely polynomial, we obtain collapses to the corresponding randomized classes in the multiple access model. In addition, we prove that there is no sparse hard set for NP under two-sided error randomized polynomial-time bounded truth-table reductions with confidence at least inversely polynomial unless NP = RP. %A van Melkebeek, Dieter %A Ogihara, Mitsunori %T Sparse Hard Sets for P %D September 11, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-40 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-40.ps.gz %X Sparse hard sets for complexity classes has been a central topic for two decades. The area is motivated by the desire to clarify relationships between completeness/hardness and density of languages and studies the existence of sparse complete/hard sets for various complexity classes under various reducibilities. Very recently, we have seen remarkable progress in this area for low-level complexity classes. In particular, the Hartmanis' sparseness conjectures for P and NL have been resolved. This article overviews the history of sparse hard set problems and exposes some of the recent results. %A Boros, E. %A Gurvich, V. %T A corrected version of the Duchet Kernel Conjecture %D September 13, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-41 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-41.ps.gz %X In 1980 Piere Duchet conjectured that odd directed cycles are the only edge minimal kernel-less connected digraphs i.e. in which after the removal of any edge a kernel appears. Although this conjecture was disproved recently by Apartsin, Ferapontova and Gurvich (1996), the following modification of Duchet's conjecture still holds: odd holes (i.e. odd non-directed chordless cycles of length 5 or more) are the only connected graphs which are not kernel-solvable but after the removal of any edge the resulting graph is kernel-solvable. %A Subramanian, Balakrishna %A Barkema, G.T. %A Lebowitz, J.L. %A Speer, E.R. %T Numerical study of a non-equilibrium interface model %D September 20, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-42 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-42.ps.gz %X We have carried out extensive computer simulations of one-dimensional models related to the low noise (solid-on-solid) non-equilibrium interface of a two dimensional anchored Toom model with unbiased and biased noise. For the unbiased case the computed fluctuations of the interface in this limit provide new numerical evidence for the logarithmic correction to the subnormal $L^{\frac{1}{2}}$ variance which was predicted by the dynamic renormalization group calculations on the modified Edwards-Wilkinson equation. In the biased case the simulations are in close quantitative agreement with the predictions of the Collective Variable Approximation (CVA), which gives the same $L^{\frac{2}{3}}$ behavior of the variance as the KPZ equation. %A Erdos, Peter L. %A Steel, Michael A. %A Szekely, Laszlo A. %A Warnow, Tandy J. %T Local quartet splits of a binary tree infer all quartet splits via one dyadic inference rule %D September 24, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-43 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-43.ps.gz %X A significant problem in phylogeny is to reconstruct a \slb\ tree from few valid quartet splits of it. It is well-known that every \slb\ tree is determined by its set of all valid quartet splits. Here we strengthen this result by showing that its local (i.e. small diameter) quartet splits infer by a dyadic inference rule all valid quartet splits, and hence determine the tree. The results of the paper also present a polynomial time algorithm to recover the tree. %A Karpinski, Marek %A Macintyre, Angus %T Polynomial Bounds for VC Dimension of Sigmoidal and General Pfaffian Neural Networks %D October 15, 1996 %Z Mon, 25 Nov 1996 15:27:22 GMT %I DIMACS %R 96-44 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-44.ps.gz %X We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the first time, that the VC Dimension of analog neural networks with the sigmoidal activation function $\sigma(y) = 1/1+e^{-y}$ is bounded by a quadratic polynomial $O((lm)^2)$ in both the number $l$ of programmable parameters, and the number $m$ of nodes. The proof method of this paper generalizes to much wider class of Pfaffian activation functions and formulas, and gives also for the first time polynomial bounds on their VC Dimension. We present also some other applications of our method. %A Grigoriev, Dima %A Karpinski, Marek %A Heide, Friedhelm Meyer auf der %T A Lower Bound for Randomized Algebraic Decision Trees %D October 15, 1996 %Z Mon, 25 Nov 1996 15:27:22 GMT %I DIMACS %R 96-45 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-45.ps.gz %X We extend the lower bounds on the depth of algebraic decision trees to the case of {\em randomized} algebraic decision trees (with two-sided error) for languages being finite unions of hyperplanes and the intersections of halfspaces, solving a long standing open problem. As an application, among other things, we derive, for the first time, an $\Omega(n^2)$ {\em randomized} lower bound for the {\em Knapsack Problem} which was previously only known for deterministic algebraic decision trees. It is worth noting that for the languages being finite unions of hyperplanes our proof method yields also a new elementary technique for deterministic algebraic decision trees without making use of Milnor's bound on Betti number of algebraic varieties. %A Ablayev, Farid %A Karpinski, Marek %T On the Power of Randomized Branching Programs %D October 15, 1996 %Z Mon, 25 Nov 1996 15:27:22 GMT %I DIMACS %R 96-46 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-46.ps.gz %X We define the notion of a randomized branching program in the natural way similar to the definition of a randomized circuit. We exhibit an explicit function $f_{n}$ for which we prove that:

1) $f_{n}$ can be computed by polynomial size randomized read-once ordered branching program with a small one-sided error;

2) $f_{n}$ cannot be computed in polynomial size by deterministic read-once branching programs;

3) $f_{n}$ cannot be computed in polynomial size by deterministic read-$k$-times ordered branching program for $k=o(n/\log n)$ (the required deterministic size is $\exp\left(\Omega\left(\frac{n}{k}\right)\right)$). %A Glebov, N. I. %A Kostochka, A. V. %T On independent domination number of graphs with given minimum degree %D October 22, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-47 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-47.ps.gz %X We prove a new upper bound on the independent domination number of graphs in terms of the number of vertices and the minimum degree. This bound is slightly better than that by J.~Haviland~\cite{H} and settles Case $\de =2$ of the corresponding conjecture by O.~Favaron~\cite{F}. %A Farach, Martin %T Optimal Suffix Tree Construction with Large Alphabets %D October 28, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-48 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-48.ps.gz %X The suffix tree of a string is the fundamental data structure of combinatorial pattern matching. In this paper, we present a novel, deterministic algorithm for the construction of suffix trees. We settle the main open problem in the construction of suffix trees: we build suffix trees in linear time for integer alphabet. %A Bellantoni, Stephen J. %T Ranking Arithmetic Proofs by Implicit Ramification %D November 7, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-49 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-49.ps.gz %X Proofs in an arithmetic system are ranked according to a ramification hierarchy based on occurrences of induction. It is shown that this ranking of proofs corresponds exactly to a natural ranking of the primitive recursive functions based on occurrences of recursion. A function is provably convergent using a rank $r$ proof, if and only if it is a rank $r$ function. The result is of interest to complexity theorists, since rank one corresponds to polynomial time. Remarkably, this characterization of polynomial-time provability admits induction over formulas having arbitrary quantifier complexity. %A Bellantoni, Stephen J. %T Ranking Primitive Recursions: the Low Grzegorczyk Classes Revisited %D November 7, 1996 %Z Mon, 11 Nov 1996 15:27:22 GMT %I DIMACS %R 96-50 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-50.ps.gz %X Traditional results in subrecursion theory are integrated with the recent work in ``predicative recursion'' by defining a simple ranking $\rho$ of all primitive recursive functions. The hierarchy defined by this ranking coincides with the Grzegorczyk hierarchy at and above the linear-space level. Thus, the result is like an extension of the Schwichtenberg/M\"uller theorems. A natural series of classes is also obtained down to the first level when primitive recursion is replaced by recursion on notation. This paper is a companion to the author's work showing how to use a suitable definition of proof rank to define weak subsystems of arithmetic containing unbounded inductions. %A Loewenstern, David %A Yianilos, Peter N. %T Significantly Lower Entropy Estimates for Natural DNA Sequences %D December 2, 1996 %Z Fri, 6 Dec 1996 15:21:23 GMT %I DIMACS %R 96-51 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-51.ps.gz %X If DNA were a random string over its alphabet {A,C,G,T},96-50.html an optimal code would assign 2 bits to each nucleotide. We imagine DNA to be a highly ordered, purposeful molecule, and might therefore reasonably expect statistical models of its string representation to produce much lower entropy estimates. Surprisingly this has not been the case for many natural DNA sequences, including portions of the human genome. We introduce a new statistical model (compression algorithm), the strongest reported to date, for naturally occurring DNA sequences. Conventional techniques code a nucleotide using only slightly fewer bits (1.90) than one obtains by relying only on the frequency statistics of individual nucleotides (1.95). Our method in some cases increases this gap by more than five-fold (1.66) and may lead to better performance in microbiological pattern recognition applications.

One of our main contributions, and the principle source of these improvements, is the formal inclusion of inexact match information in the model. The existence of matches at various distances forms a panel of experts which are then combined into a single prediction. The structure of this combination is novel and its parameters are learned using Expectation Maximization (EM).

Experiments are reported using a wide variety of DNA sequences and compared whenever possible with earlier work. Four reasonable notions for the string distance function used to identify near matches, are implemented and experimentally compared.

We also report lower entropy estimates for coding regions extracted from a large collection of non-redundant human genes. The conventional estimate is 1.92 bits. Our model produces only slightly better results (1.91 bits) when considering nucleotides, but achieves 1.84-1.87 bits when the prediction problem is divided into two stages: i) predict the next amino acid based on inexact polypeptide matches, and ii) predict the particular codon. Our results suggest that matches at the amino acid level play some role, but a small one, in determining the statistical structure of non-redundant coding sequences. %A Grigoriev, Dima %A Karpinski, Marek %T Randomized Omega (n^2) Lower Bound for Knapsack %D December 3, 1996 %Z Fri, 6 Dec 1996 15:20:19 GMT %I DIMACS %R 96-52 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-52.ps.gz %X We prove Omega (n^2) complexity lower bound for the general model of randomized computation trees solving the Knapsack Problem, and more generally Restricted Integer Programming. This is the first nontrivial lower bound proven for this model of computation. The method of the proof depends crucially on the new technique for proving lower bounds on the border complexity of a polynomial which could be of independent interest. %A Durand, Dannie %A Farach, Martin %T On the Design of Optimization Criteria for Multiple Sequence Alignment %D December 10, 1996 %Z Fri, 3 Jan 1997 15:12:03 GMT %I DIMACS %R 96-53 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-53.ps.gz %X Multiple sequence alignment (MSA) is important in functional, structural and evolutionary studies of sequence data. Much research has focussed on posing MSA as an optimization problem, and several optimization criteria have been explored. In this paper, we discuss biological and mathematical problems that arise in cost function design for the multiple sequence alignment problem. In particular, we focus on tree alignment, which is often viewed as the most ``biological'' of the rigorous approaches to MSA. We point out several important pitfalls in current optimization approaches to MSA and identify characteristics for good cost function design. We address some extra design issues specific to approximation algorithms. We hope these ideas will lead to future research on a biologically realistic and mathematically rigorous approach to MSA. %A Karpinski, Marek %A Larmore, Lawrence L. %A Rytter, Wojciech %T Correctness of Constructing Optimal Alphabetic Trees Revisited %D December 10, 1996 %Z Fri, 31 Jan 1997 11:20:15 GMT %I DIMACS %R 96-54 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-54.ps.gz %X Several new observations which lead to new correctness proofs of two known algorithms (Hu-Tucker and Garsia-Wachs) for construction of optimal alphabetic trees are presented. A generalized version of the Garsia-Wachs algorithm is given. Proof of this generalized version works in a structured and illustrative way and clarifies the usually poorly-understood behavior of both the Hu-Tucker and Garsia-Wachs algorithms. The generalized version permits any non-negative weights, as opposed to strictly positive weights required in the original Garsia-Wachs algorithm. New local structural properties of optimal alphabetic trees are given. The concept of {\em well-shaped segment\/} (a part of an optimal tree) is introduced. It is shown that some parts of the optimal tree are known in advance to be well-shaped, and this implies correctness of the algorithms rather easily. The crucial part of the correctness proof of the Garsia-Wachs algorithm, namely the {\em structural theorem}, is identified. The correctness proof of the Hu-Tucker algorithm consists of showing a very simple mutual simulation between this algorithm and the Garsia-Wachs algorithm. For this proof, it is essential to use the generalized version of Garsia-Wachs algorithm, in which an arbitrary locally minimal pair is processed, not necessarily the rightmost minimal pair. Such a generalized version is also needed for parallel implementations. Another result presented in this paper is the clarification of the problem of resolving ties (equalities between weights of items) in the Hu-Tucker algorithm. This is related to the proof, by simulation, of correctness of the Hu-Tucker algorithm. It is shown that the condition that there are no ties may generally be assumed without harm and that, essentially, the Hu-Tucker algorithm avoids ties automatically. %A Valtr, Pavel %T On galleries with no bad points %D December 17, 1996 %Z Thu, 19 Dec 1996 16:27:22 GMT %I DIMACS %R 96-55 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-55.ps.gz %X For any $k$ we construct a simply connected compact set (art gallery) in $R^3$ whose every point sees a positive fraction (in fact, more than $5/9$) of the gallery, but the whole gallery cannot be guarded by $k$ guards. This disproves a conjecture of Kavraki, Latombe, Motwani, and Raghavan. %A Koiran, Pascal %A Sontag, Eduardo D. %T Vapnik-Chervonenkis Dimension of Recurrent Neural Networks %D December 19, 1996 %Z Thu, 19 Dec 1996 16:27:18 GMT %I DIMACS %R 96-56 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-56.ps.gz %X Most of the work on the Vapnik-Chervonenkis dimension of neural networks has been focused on feedforward networks. However, recurrent networks are also widely used in learning applications, in particular when time is a relevant parameter. This paper provides lower and upper bounds for the VC dimension of such networks. Several types of activation functions are discussed, including threshold, polynomial, piecewise-polynomial and sigmoidal functions. The bounds depend on two independent parameters: the number $w$ of weights in the network, and the length $k$ of the input sequence. In contrast, for feedforward networks, VC dimension bounds can be expressed as a function of $w$ only. An important difference between recurrent and feedforward nets is that a fixed recurrent net can receive inputs of arbitrary length. Therefore we are particularly interested in the case~$k \gg w$. Ignoring multiplicative constants, the main results say roughly the following: \begin{itemize} \item For architectures with activation $\sigma $ = any fixed nonlinear polynomial, the VC dimension is $\approx \nopar\leninp$. \item For architectures with activation $\sigma $ = any fixed {\it piecewise\/} polynomial, the VC dimension is between $\nopar\leninp$ and $\nopar^2\leninp$. \item For architectures with activation $\sigma = {\cal H}$ (threshold nets), the VC dimension is between $\nopar\log(\leninp/\nopar)$ and $\min\{\nopar\leninp\log\nopar\leninp,\nopar^2+\nopar\log\nopar\leninp\}$. \item For the standard sigmoid $\sigma(x)=1/(1+e^{-x})$, the VC dimension is between $\nopar\leninp$ and $\nopar^4\leninp^2$. \ei %A Rodl, Vojtech %A Thoma, Lubos %T On the Size of Set Systems on [n] Not Containing Weak (r, \Delta)-Systems %D December 19, 1996 %Z Mon, 24 Feb 1997 20:41:55 GMT %I DIMACS %R 96-57 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-57.ps.gz %X Let $r\ge 3$ be an integer. A weak $(r, \Delta)$-system is a family of $r$ sets such that all pairwise intersections among the members have the same cardinality.

We show that for $n$ large enough, there exists a family ${\cal F}$ of subsets of $[n]$ such that ${\cal F}$ does not contain a weak $(r, \Delta)$-system and $|{\cal F}| \ge 2^{ {1\over 3} \cdot n^{1/5}\log^{4/5}(r-1)}.$

This improves an earlier result of P. Erd\H{o}s and E. Szemer\'edi. %A Frieze, Alan %A Karonski, Michal %A Thoma, Lubos %T On Perfect Matchings and Hamiltonian Cycles in Sums of Random Trees %D December 19, 1996 %Z Mon, 24 Feb 1997 20:46:05 GMT %I DIMACS %R 96-58 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-58.ps.gz %X We prove that the sum of two random trees almost surely possesses a perfect matching and the sum of five random trees almost surely possesses a Hamiltonian cycle. %A Karpinski, Marek %A Zelikovsky, Alexander %T Approximating Dense Cases of Covering Problems %D December 20, 1996 %Z Tue, 11 Feb 1997 14:17:25 GMT %I DIMACS %R 96-59 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-59.ps.gz %X We study dense cases of several covering problems. An instance of the set cover problem with $m$ sets is dense if there is $\epsilon>0$ such that any element belongs to at least $\epsilon m$ sets. We show that the dense set cover problem can be approximated with the performance ratio $c\log n$ for any $c>0$ and it is unlikely to be NP-hard. We construct a polynomial-time approximation scheme for the dense Steiner tree problem in $n$-vertex graphs, i.e. for the case when each terminal is adjacent to at least $\epsilon n$ vertices. We also study the vertex cover problem in $\epsilon$-dense graphs. Though thisproblem is shown to be still MAX-SNP-hard as in general graphs, we find a better approximation algorithm with the performance ratio $2\over{1+\epsilon}$. The {\em superdense} cases of all these problems are shown to be solvable in polynomial time. %A DIMACS %T DIMACS SPECIAL YEAR IN MATHEMATICAL SUPPORT FOR MOLECULAR BIOLOGY ANNUAL REPORT JANUARY 1996 %D February 6, 1997 %Z Thu, 6 Feb 1997 19:02:40 GMT %I DIMACS %R 96-60 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-60.ps.gz %X No abstract. %A DIMACS %T DIMACS ANNUAL REPORT - DECEMBER 1996 %D February 27, 1997 %Z Wed, 27 Feb 1997 20:38:55 GMT %I DIMACS %R 96-61 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-61.ps.gz %X No abstract. %A Jain, R. %A Werth, J. %T Analysis of approximate algorithms for constrained and unconstrained edge-coloring of bipartite graphs %D April 7, 1995 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 95-01 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1995/95-01.ps.gz %X The problem of edge-coloring a bipartite graph is to color the edges so that adjacent edges receive different colors. An optimal algorithm uses the minimum number of colors to color the edges. We consider several approximation algorithms for edge-coloring bipartite graphs and show tight bounds on the number of colors they use in the worst case. We also briefly consider the constrained edge-coloring problem where each color may be used to color at most $k$ edges, and obtain bounds on the number of colors used by the approximation algorithms in the worst case. %A Ramana, Motakuri %T An Exact Duality Theory for Semidefinite Programming and its Complexity Implications %D April 10,1995 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 95-02 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1995/95-02R.ps.gz %X In this paper, we present a new and more complete duality for Semidefinite Programming (SDP), with the following features: \begin{itemize} \item This dual is an explicit semidefinite program, whose number of variables and the coefficient bitlengths are polynomial in those of the primal. \item If the Primal is feasible, then it is bounded if and only if the dual is feasible. \item The duality gap, \ie the difference between the primal and the dual objective function values, is zero whenever the primal is feasible and bounded. Also, in this case, the dual attains its optimum \item It yields a precise Farkas Lemma for semidefinite feasibility systems, \ie characterization of the {\it infeasibility} of a semidefinite inequality in terms of the {\it feasibility} of another polynomial size semidefinite inequality. \end{itemize} Note that the standard duality for Linear Programming satisfies all of the above features, but no such duality theory was previously known for SDP, without Slater-like conditions being assumed. Then we apply the dual to derive certain complexity results for Semidefinite Programming Problems. The decision problem of Semidefinite Feasibility (SDFP), \ie that of determining if a given semidefinite inequality system is feasible, is the central problem of interest. The complexity of SDFP is unknown, but we show the following: 1) In the Turing machine model, SDFP is not NP-Complete unless NP=Co-NP; 2) In the real number model of Blum, Shub and Smale\cite{bss}, SDFP is in NP$\cap$Co-NP. We then give polynomial reductions from the following problems to SDFP: 1) Checking whether an SDP is bounded; 2) Checking whether a feasible and bounded SDP attains the optimum; 3) Checking the optimality of a feasible solution. %A Correa, Ricardo %A Ferreira, Afonso %T Parallel Best-First Branch-and-Bound in Discrete Optimization %D April 10, 1995 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 95-03 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1995/95-03.ps.gz.ps %X In this report, parallelism is used as a way to solve {\em discrete optimization problems}. We search for an {\em optimal solution} $x^{*}\in S^{*}$, where $S^{*}$ is the set of all best solutions in a {\em % domain} $S$, defined as the discrete set of all vectors $x$ in the solution space that satisfy a set of constraints. Improving the search efficiency is of considerable importance since exhaustive search is often impracticable. The method called {\em % branch-and-bound} (noted B\&B) is a tree search algorithm often used as an intelligent search in this context. Its principle lies in successive decompositions of the original problem in smaller disjoint subproblems until an optimal solution is found. The algorithm consists of a heuristic itn this context. Its principle lies in successive decompositions of the original problem in smaller disjoint subproblems until an optimal solution is found. The algorithm consists of a heuristic iterative search that avoids visiting some subproblems which are known not to contain an optimal solution. Parallel processing has been widely studied as an additional source of improvement in search efficiency in discrete optimization. We review in this report the literature pertinent to {\em parallel branch-and-bound algorithms}. The focus is on {\em distributed memory} parallel systems, which are composed of a set of processors connected by a physical network, each one with its own local memory. The communications between two different processors are implemented through the exchange of messages over links of the network connecting the two processors. Given that an attractive feature is that disjoint subproblems can be decomposed simultaneously and independently, the challenge is how to use the set of processors to improve the search efficiency of B\&B algorithms, concurrently decomposing several subproblems at each iteration. In general terms, the potential to be explored consists of a linear -- on the number of processors -- reduction on the number of iterations. However, the reduction on the number of iterations can deviate considerably from linear due to possible {\em % speedup anomalies}. Parallel B\&B is traditionally considered as an irregular parallel algorithm due to the fact that the structure of the search tree is not known beforehand. It may result in unnecessary work if a subproblem that does not contain an optimal solution is chosen and assigned to a processor to be decomposed. Therefore, the use of a distributed memory parallel system incurs a number of overheads, including communication overheads and idle time due to workload imbalance and contention on common data structures. Several special techniques have been developed to address these problems, essentially related to the amount of ``necessary'' work assigned to each processor. This report reviews these techniques, attempting to tie the area of parallel B\&B under a common, uniform terminology. It can be profitable both to the parallel processing and to the operations research community members. %A Lowenstern, D. %A Hirsh, H. %A Noordiwier, M. %A Yianilos, P. %T DNA Sequence Classification Using Compression-Based Induction %D May 1, 1995 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 95-04 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1995/95-04.ps.gz %X Inductive learning methods, such as neural networks and decision trees, have become a popular approach to developing DNA sequence identification tools. Such methods attempt to form models of a collection of training data that can be used to predict future data accurately. The common approach to using such methods on DNA sequence identification problems forms models that depend on the {\em absolute locations} of nucleotides and assume {\em independence} of consecutive nucleotide locations. This paper describes a new class of learning methods, called {\em compression-based induction} (CBI), that is geared towards sequence learning problems such as those that arise when learning DNA sequences. The central idea is to use text compression techniques on DNA sequences as the means for generalizing >from sample sequences. The resulting methods form models that are based on the more important {\em relative locations} of nucleotides and on the {\em dependence} of consecutive locations. They also provide a suitable framework into which biological domain knowledge can be injected into the learning process. We present initial explorations of a range of CBI methods that demonstrate the potential of our methods for DNA sequence identification tasks. %A Applegate, D. %A Bixby, R. %A Chvatal, V. %A Cook, B. %T Finding Cuts in the TSP (A preliminary report) %D April 10, 1995 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 95-05 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1995/95-05.ps.gz %X TSPLIB is Gerhard Reinelt's library of some hundred instances of the traveling salesman problem. Some of these instances arise from drilling holes in printed circuit boards; others arise from X-ray crystallography; yet others have been constructed artificially. None of them (with a single exception) is contrived to be hard and none of them is contrived to be easy; their sizes range from 17 to 85,900 cities; some of them have been solved and others have not. We have solved twenty previously unsolved problems from the TSPLIB. One of them is the problem with 225 cities that was contrived to be hard; the sizes of the remaining nineteen range from 1,000 to 7,397 cities. Like all the successful computer programs for solving the TSP, our computer program follows the scheme designed by George Dantzig, Ray Fulkerson, and Selmer Johnson in the early nineteen-fifties. The purpose of this preliminary report is to describe *some* of our innovations in implementing the Dantzig-Fulkerson-Johnson scheme; we are planning to write up a more comprehensive account of our work soon. %A Dubchack, I. %A Mayoraz, E. %A Muchnik, I. %T Relation between Protein Structure, Sequence Homology and Composition of Amino Acids %D April 10, 1995 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 95-06 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1995/95-06.ps.gz %X A method of quantitative comparison of two classifications rules applied to protein folding problem is presented. Classification of proteins based on sequence homology and based on amino acid composition were compared and analyzed according to this approach. The coefficient of correlation between these classification methods and the procedure of estimation of robustness of the coefficient are discussed. %A Romanik, K. %T Directed Rectangle-Visibility Graphs have Unbounded Dimension %D April 17, 1995 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 95-07 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1995/95-07.ps.gz %X Visibility representations of graphs map vertices to sets in Euclidean space and express edges as visibility relations between these sets. One visibility representation in the plane that has been studied is one in which the vertices of the graph map to closed isothetic rectangles and the edges are expressed by horizontal or vertical visibility between the rectangles. Two rectangles are only considered to be visible to one another if there is a non-zero width horizontal orvertical band of sight between them. A graph that can be represented in this way is called a rectangle-visibility graph. A rectangle-visibility graph can be directed by directing all edges towards the positive x and y directions, which yields a directed acyclic graph. A directed acyclic graph G has dimension d if d is the minimum integer such that the vertices of G can be ordered by d linear orderings, <_1, ..., <_d, and for vertices u and v there is a directed path from u to v if and only if u <_i v for all 1 <= i <= d. In this note we show that the dimension of the class of directed rectangle-visibility graphs is unbounded. %A Pekec, A. %T Optimization under Ordinal Scales: When is a Greedy Solution Optimal? %D April 18, 1995 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 95-08 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1995/95-08.ps.gz %X Mathematical formulation of an optimization problem often depends on data which can be measured in more than one acceptable way. If the conclusion of optimality depends on the choice of measure, then we should question whether it is meaningful to ask for an optimal solution. If meaningful optimal solution exists and the objective function depends on data measured on an ordinal scale of measurement, then the greedy algorithm will give such a solution for a wide range of objective functions. %A Rothkopf, M.H. %A Pekec, A. %A Harstad, R.M. %T Computationally Manageable Combinatorial Auctions %D April 19, 1995 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 95-09 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1995/95-09.ps.gz %X There is interest in designing simultaneous auctions for situations in which the value of assets to a bidder depends upon which other assets he or she wins. In such cases, bidders may well wish to submit bids for combinations of assets. When this is allowed, the problem of determining the revenue maximizing set of nonconflicting bids can be a difficult one. We analyze this problem, identifying several different structures of combinatorial bids for which computational tractability is constructively demonstrated and some structures for which computational tractability cannot be guaranteed. %A Pekec, A. %T A Winning Strategy for the Ramsey Graph Game %D April 21, 1995 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 95-10 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1995/95-10.ps.gz %X We consider a "Maker-Breaker" version of the Ramsey Graph Game, RG(n), and present a winning strategy for maker requiring less than n(2^n) moves. This is the fastest winning strategy known so far. We also demonstrate how the ideas presented can be used to develop winning strategies for some related combinatorial games. %A Jain, R. %A Werth, J. %T Airdisks and AirRAID: Modeling and scheduling periodic wireless data broadcast %D June 15, 1995 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 95-11 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1995/95-11.ps.gz %X We introduce a simple model, called the airdisk, for modeling the access of data transmitted periodically over wireless media as being analogous to the access of data from a standard magnetic disk. We consider several issues related to airdisks, such as their mean rotational latency under certain assumptions. The problem of scheduling the order in which data items are broadcast is analogous to that of determining how data should be laid out on the disk. Two problems of laying out data so as to minimize read time, given information about which data items are of most interest to the clients, are defined; both are shown to be NP-complete. We discuss ways in which the information about which items are of interest to clients can be obtained. Finally we consider how to increase the performance and storage capacity of airdisks, using the magnetic disk analogy as a guide. We suggest using multiple-track airdisks or borrowing the idea of Redundant Arrays of Inexpensive Disks (RAID) which is used for magnetic disks; for the wireless data broadcast environment we call the latter approach airRAID. %A Thorup, M. %T Equivalence between sorting and priority queues %D May 30, 1995 %Z Mon, 14 Sep 1998 20:00:00 GMT %I DIMACS %R 95-12 %U ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1995/95-12.ps.gz %X For a RAM with arbitrary word size, it is shown that if we can sort n integers, each contained in one word, in time n*s(n), then (and only then) there is a priority queue with capacity for n integers, supporting `find-min' in constant time and `insert' and `delete' in `s(n)+0(1)$ amortized time. Here it is required that when we insert a key, it is not smaller than the current smallest key. The equivalence holds even if n is limited in terms of the word size w. One application is an O(n(log n)^{1/2+e} + m), e>0, algorithm for the single source sh