{"paper":{"title":"Approximation Algorithm for the Partial Set Multi-Cover Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DM","authors_text":"Ding-Zhu Du, Guangmo Tong, James Willson, Yingli Ran, Yishuo Shi, Zhao Zhang","submitted_at":"2018-11-20T11:25:54Z","abstract_excerpt":"Partial set cover problem and set multi-cover problem are two generalizations of set cover problem. In this paper, we consider the partial set multi-cover problem which is a combination of them: given an element set $E$, a collection of sets $\\mathcal S\\subseteq 2^E$, a total covering ratio $q$ which is a constant between 0 and 1, each set $S\\in\\mathcal S$ is associated with a cost $c_S$, each element $e\\in E$ is associated with a covering requirement $r_e$, the goal is to find a minimum cost sub-collection $\\mathcal S'\\subseteq\\mathcal S$ to fully cover at least $q|E|$ elements, where element"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08185","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":""},"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"}