Abstract:We study the complexity of determining the edge connectivity of a simple graph with cut queries. We show that (i) there is a bounded-error randomized algorithm that computes edge connectivity with O(n) cut queries, and (ii) there is a bounded-error quantum algorithm that computes edge connectivity with Õ( √ n) cut queries. To prove these results we introduce a new technique, called star contraction, to randomly contract edges of a graph while preserving nontrivial minimum cuts. In star contraction vertices ran… Show more
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