### DIMACS Theoretical Computer Science Seminar

Title: Testing Orientations

Speaker: **Ilan Newman**, University of Haifa

Date: September 13, 2005 2:00-3:00pm

Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

We propose a new testing model for studying some graph related problems
that we call the orientation model. In this model, an undirected
graph $G$ is fixed, and the input is any possible edge orientation
of $G$. A property is now a property of the directed graph that is
obtained under a given orientation. The distance between two
orientations is the number of edges that have to be redirected in
order to move from one digraph to the other (thus, we do not allow
deletions or insertions).

This model allows studying properties such as not containing a
forbidden (induced) subgraph, being strongly connected etc., for
every underlying graph including sparse graphs. As it turns out,
this model strictly generalizes the standard, adjacency matrix,
model. That is, we show that for every graph property $P$
of dense graphs in the standard model, there is a property of
orientation that if testable by a 1-sided error tester, then so is
$P$ . This model is also handy in some practical
situations of networks, in which the underlying network is fixed
while the direction of (weighted) links may vary.

We show that several orientations properties are testable in this
model (for every underlying graph) (etc. being drain-source-free),
while some are not.

This is joint work with Shirley Halevi, Oded Lachish and Dekel Tsur.