Randomized sequential importance sampling for estimating the number of perfect matchings in bipartite graphs

07/04/2019

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by   Persi Diaconis, et al.

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We introduce novel randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we prove various non-standard central limit theorems, via limit theory for random variables satisfying distributional recurrence relations of divide-and-conquer type. We expect that our methods will be useful for other applied problems, such as counting and testing for contingency tables or graphs with given degree sequence.