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
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.