{"paper":{"title":"Maximizing Sums of Non-monotone Submodular and Linear Functions: Understanding the Unconstrained Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Kobi Bodek, Moran Feldman","submitted_at":"2022-04-07T12:52:30Z","abstract_excerpt":"Motivated by practical applications, recent works have considered maximization of sums of a submodular function $g$ and a linear function $\\ell$. Almost all such works, to date, studied only the special case of this problem in which $g$ is also guaranteed to be monotone. Therefore, in this paper we systematically study the simplest version of this problem in which $g$ is allowed to be non-monotone, namely the unconstrained variant, which we term Regularized Unconstrained Submodular Maximization (RegularizedUSM).\n  Our main algorithmic result is the first non-trivial guarantee for general Regul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.03412","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/2204.03412/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"}