The Power of Local Marginals: An $O(\varepsilon^{-1})$-Aspect-Ratio Reduction for Dynamic Weighted Matching

[2608.27805] The Power of Local Marginals: An $O(\varepsilon^{-1})$-Aspect-Ratio Reduction for Dynamic Weighted Matching Skip to main content Search Submit Donate Log in Computer Science > Data Structures and Algorithms arXiv:2608.27805 (cs) [Submitted on 28 Aug 2026 ( v1 ), last revised 7 Oct 2026 (this version, v2)] Title: The Power of Local Marginals: An $O(\varepsilon^{-1})$-Aspect-Ratio Reduction for Dynamic Weighted Matching Authors: Jiale Chen View PDF HTML (experimental) Abstract: We study dynamic maximum weight matching under edge insertions and deletions in two settings: maintaining a $(1\pm\varepsilon)$-approximation to the optimum weight, and maintaining an explicit $(1-\varepsilon)$-approximate matching. Our main result is a reduction that transforms instances of polynomial aspect ratio into instances of aspect ratio $O(\varepsilon^{-1})$. The reduction applies to general graphs in both settings and is compatible with partially dynamic updates. The reduction is based on a structural property of local marginals. After grouping edges into weight classes, the global marginal contribution of one class relative to all lower classes is approximated by its marginal contribution within a local weight window of aspect ratio $O(\varepsilon^{-1})$. Summing these local marginals yields a value composition lemma that approximates the optimum weight in the entire graph with approximate optimum weights of the local windows. This improves the value reduction of Gupta and Peng (FOCS 2013), whose local aspect ratio is $\varepsilon^{-\Theta(\varepsilon^{-1})}$. The same structural property yields an improved matching composition lemma for explicit matchings, reducing the local aspect ratio of Bernstein--Chen--Dudeja--Langley--Sidford--Tu (SODA 2025) from $O(\varepsilon^{-2})$ to $O(\varepsilon^{-1})$. Comments: To appear in SOSA 2027 Subjects: Data Structures and Algorithms (cs.DS) Cite as: arXiv:2608.27805 [cs.DS] (or arXiv:2608.27805v2 [cs.DS] for this version) https://doi.org/10.48550/arXiv.2608.27805 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jiale Chen [ view email ] [v1] Fri, 28 Aug 2026 00:46:09 UTC (33 KB) [v2] Wed, 7 Oct 2026 17:44:35 UTC (33 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.DS < prev | next > new | recent | 2026-08 Change to browse by: cs References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from (opens in new tab) (opens in new tab) (opens in new tab)

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