{"paper":{"title":"Submodular Maximization over Many Matroids via Ordered Local Search","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Neta Singer, Theophile Thiery","submitted_at":"2026-07-01T12:09:41Z","abstract_excerpt":"Given a monotone submodular function, we consider the problem of finding a maximum-valued set in the intersection of $k$ matroids. Our main result is a polynomial time local search based algorithm achieving a $\\frac{k}{2} + o(k)$ approximation guarantee. This asymptotically matches the best-known guarantee of $\\frac{k}{2} + \\epsilon$ in the unweighted setting by Lee, Sviridenko, and Vondr\\'ak (2009). Prior to this work, the state-of-the-art was a $\\frac{\\ln(4)k}{1+\\ln(2)} + o(k)$-approximation algorithm obtained by Feldman and Ward (2026). Our approach extends to Matroid $k$-Parity yielding th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00843","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.00843/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}