{"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/nearly-linear-time-parallelizable-algorithms","title":"Practical and Parallelizable Algorithms for Non-Monotone Submodular Maximization with Size Constraint","arxiv_id":"2009.01947","date":"2020-09-03","proceeding":null,"authors":["Yixin Chen","Alan Kuhnle"],"abstract":"We present combinatorial and parallelizable algorithms for maximization of a submodular function, not necessarily monotone, with respect to a size constraint. We improve the best approximation factor achieved by an algorithm that has optimal adaptivity and nearly optimal query complexity to $0.193 - \\varepsilon$. The conference version of this work mistakenly employed a subroutine that does not work for non-monotone, submodular functions. In this version, we propose a fixed and improved subroutine to add a set with high average marginal gain, ThreshSeq, which returns a solution in $O( \\log(n) )$ adaptive rounds with high probability. Moreover, we provide two approximation algorithms. The first has approximation ratio $1/6 - \\varepsilon$, adaptivity $O( \\log (n) )$, and query complexity $O( n \\log (k) )$, while the second has approximation ratio $0.193 - \\varepsilon$, adaptivity $O( \\log^2 (n) )$, and query complexity $O(n \\log (k))$. Our algorithms are empirically validated to use a low number of adaptive rounds and total queries while obtaining solutions with high objective value in comparison with state-of-the-art approximation algorithms, including continuous algorithms that use the multilinear extension.","url_abs":"https://arxiv.org/abs/2009.01947v5","url_pdf":"https://arxiv.org/pdf/2009.01947v5.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":"abstracts"},"code_links":[{"paper_slug":"nearly-linear-time-parallelizable-algorithms","repo_url":"https://gitlab.com/luciacyx/nm-adaptive-code","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":"https://app.syntology.ai/?focus=2009.01947","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}