Abstract:This paper makes three contributions to estimating the number of perfect matching in bipartite graphs. First, we prove that the popular sequential importance sampling algorithm works in polynomial time for dense bipartite graphs. More carefully, our algorithm gives a (1 − )-approximation for the number of perfect matchings of a λ-dense bipartite graph, using) samples. With size n on each side and for 1 2 > λ > 0, a λ-dense bipartite graph has all degrees greater than (λ + 1 2 )n. Second, practical applications… Show more
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