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.

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