{"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/an-unrestricted-faster-algorithm-for-maximum","title":"A Faster Algorithm for Maximum Weight Matching on Unrestricted Bipartite Graphs","arxiv_id":"2502.20889","date":"2025-02-28","proceeding":null,"authors":["Shawxing Kwok"],"abstract":"Given a weighted bipartite graph $G = (L, R, E, w)$, the maximum weight matching (MWM) problem seeks to find a matching $M \\subseteq E$ that maximizes the total weight $\\sum_{e \\in M} w(e)$. This paper presents a novel algorithm with a time complexity of $O(\\min(X^3 + E, XE + X^2\\log X))$, where $X = \\min(|L|, |R|)$. Unlike many existing algorithms, our approach supports real-valued weights without additional constraints. Under this condition, our result improves upon the previous best-known bound of $O(VE + V^2\\log V)$, or more strictly $O(XE + XV\\log V)$, where $V = L \\cup R$. The suggested implementation code is simplified and publicly available at https://github.com/ShawxingKwok/Kwok-algorithm, with the average-case time complexity of $O(E^{1.4} + LR)$ estimated from experimental results on random graphs.","url_abs":"https://arxiv.org/abs/2502.20889v3","url_pdf":"https://arxiv.org/pdf/2502.20889v3.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":"an-unrestricted-faster-algorithm-for-maximum","repo_url":"https://github.com/shawxingkwok/kwok-algorithm","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}