{"paper":{"title":"A Reduction for Optimizing Lattice Submodular Functions with Diminishing Returns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG"],"primary_cat":"cs.DS","authors_text":"Alina Ene, Huy L. Nguyen","submitted_at":"2016-06-27T16:44:44Z","abstract_excerpt":"A function $f: \\mathbb{Z}_+^E \\rightarrow \\mathbb{R}_+$ is DR-submodular if it satisfies $f({\\bf x} + \\chi_i) -f ({\\bf x}) \\ge f({\\bf y} + \\chi_i) - f({\\bf y})$ for all ${\\bf x}\\le {\\bf y}, i\\in E$. Recently, the problem of maximizing a DR-submodular function $f: \\mathbb{Z}_+^E \\rightarrow \\mathbb{R}_+$ subject to a budget constraint $\\|{\\bf x}\\|_1 \\leq B$ as well as additional constraints has received significant attention \\cite{SKIK14,SY15,MYK15,SY16}.\n  In this note, we give a generic reduction from the DR-submodular setting to the submodular setting. The running time of the reduction and t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08362","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"}