Theoretical Analysis of Sequential Importance Sampling Algorithms for a Class of Perfect Matching Problems

This paper analyzes the performance of sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. Precise bounds on the number of samples required to yield an accurate estimate are derived. In doing so, moments of permutation statistics are computed using generating functions and nonstandard limit theorems are derived by expressing perfect matchings as a time-inhomogeneous Markov chain.