Testing st -Connectivity

We continue the study, started in [9], of property testing of graphs in the orientation model. A major question which was left open in [9] is whether the property of st-connectivity can be tested with a constant number of queries. Here we answer this question on the affirmative. To this end we construct a non-trivial reduction of the st-connectivity problem to the problem of testing languages that are decidable by branching programs, which was solved in [11]. The reduction combines combinatorial arguments with a concentration type lemma that is proven for this purpose. Unlike many other property testing results, here the resulting testing algorithm is highly non-trivial itself, and not only its analysis. ∗Department of Computer Science, University of Chicago, Chicago, IL-60637 USA. Email: [email protected] †Department of Computer Science, Technion, Haifa 3200, Israel. Email: [email protected] ‡Department of Computer Science, Technion, Haifa 3200, Israel. Email: [email protected] §Department of Computer Science, Technion, Haifa 3200, Israel. Email: [email protected] ¶Department of Computer Science, University of Haifa, Haifa 31905, Israel. Email: [email protected], Research supported in part by an Israel Science Foundation grant number 55/03.