Sequential importance sampling for estimating expectations over the space of perfect matchings

O(n 1−2λ 8λ + ) samples. With size n on each side and for 2 > λ > 0, a λ-dense bipartite graph has all degrees greater than (λ+ 1 2 )n. Second, practical applications of the algorithm requires many calls to matching algorithms. A novel preprocessing step is provided which makes significant improvements. Third, three applications are provided. The first is for counting Latin squares, the second is a practical way of computing the greedy algorithm for a card guessing game with feedback, and the third is for stochastic block models. In all three examples, sequential importance sampling allows treating practical problems of reasonably large sizes.

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