A Bregman-Sinkhorn Algorithm for the Maximum Weight Independent Set Problem

[2408.02086] A Bregman-Sinkhorn Algorithm for the Maximum Weight Independent Set Problem Skip to main content Search Submit Donate Log in Mathematics > Optimization and Control arXiv:2408.02086 (math) [Submitted on 4 Aug 2024 ( v1 ), last revised 24 Aug 2026 (this version, v4)] Title: A Bregman-Sinkhorn Algorithm for the Maximum Weight Independent Set Problem Authors: Stefan Haller , Bogdan Savchynskyy View PDF HTML (experimental) Abstract: We propose a scalable approximate algorithm for the NP-hard maximum-weight independent set problem, based on dual coordinate descent applied to a smoothed clique-cover LP relaxation. Our method, a variant of the Bregman/Sinkhorn algorithm, employs entropy smoothing with a novel duality-gap-based smoothing scheduling strategy that empirically outperforms standard feasibility scheduling for the relaxed problem. Our new projection to the primal feasible set enables accurate duality gap estimation. Combined with a basic primal heuristic leveraging reduced costs, our approach yields high-quality integer solutions. On real-world datasets, it efficiently finds high-quality approximate solutions for graphs with up to 882,000 nodes and 344 million edges within seconds. Subjects: Optimization and Control (math.OC) Cite as: arXiv:2408.02086 [math.OC] (or arXiv:2408.02086v4 [math.OC] for this version) https://doi.org/10.48550/arXiv.2408.02086 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Stefan Haller [ view email ] [v1] Sun, 4 Aug 2024 16:51:57 UTC (120 KB) [v2] Sat, 24 Aug 2024 21:38:50 UTC (113 KB) [v3] Tue, 25 Mar 2025 22:26:18 UTC (153 KB) [v4] Mon, 24 Aug 2026 20:06:23 UTC (152 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2024-08 Change to browse by: math 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)

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