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

## TL;DR

This paper presents randomized sequential importance sampling algorithms to estimate the number of perfect matchings in bipartite graphs, supported by new central limit theorems, with potential applications to other problems.

## Contribution

It introduces novel randomized importance sampling methods for counting perfect matchings and provides theoretical analysis through non-standard central limit theorems.

## Key findings

- Algorithms effectively estimate perfect matchings
- Theoretical analysis confirms estimator accuracy
- Potential applicability to other combinatorial problems

## Abstract

We introduce and study randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we establish various non-standard central limit theorems. We expect our methods to be useful for other applied problems.