{"paper":{"title":"Efficient Submodular Function Maximization under Linear Packing Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Iftah Gamzu, Yossi Azar","submitted_at":"2010-07-21T10:23:47Z","abstract_excerpt":"We study the problem of maximizing a monotone submodular set function subject to linear packing constraints. An instance of this problem consists of a matrix $A \\in [0,1]^{m \\times n}$, a vector $b \\in [1,\\infty)^m$, and a monotone submodular set function $f: 2^{[n]} \\rightarrow \\bbR_+$. The objective is to find a set $S$ that maximizes $f(S)$ subject to $A x_{S} \\leq b$, where $x_S$ stands for the characteristic vector of the set $S$. A well-studied special case of this problem is when $f$ is linear. This special case captures the class of packing integer programs.\n  Our main contribution is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3604","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}