{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/sequential-importance-sampling-for-estimating","title":"Sequential importance sampling for estimating expectations over the space of perfect matchings","arxiv_id":"2107.00850","date":"2021-07-02","proceeding":null,"authors":["Yeganeh Alimohammadi","Persi Diaconis","Mohammad Roghani","Amin Saberi"],"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 $(1\\pm\\epsilon)$-approximation for the number of perfect matchings of a $\\lambda$-dense bipartite graph, using $O(n^{\\frac{1-2\\lambda}{\\lambda}\\epsilon^{-2}})$ samples. With size $n$ on each side and for $\\frac{1}{2}>\\lambda>0$, a $\\lambda$-dense bipartite graph has all degrees greater than $(\\lambda+\\frac{1}{2})n$. Second, practical applications of the algorithm require 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.","url_abs":"https://arxiv.org/abs/2107.00850v2","url_pdf":"https://arxiv.org/pdf/2107.00850v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"sequential-importance-sampling-for-estimating","repo_url":"https://github.com/mohammadroghani/SIS","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}