{"paper":{"title":"On Approximating Partial Set Cover and Generalizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Chandra Chekuri, Kent Quanrud, Zhao Zhang","submitted_at":"2019-07-09T21:00:48Z","abstract_excerpt":"Partial Set Cover (PSC) is a generalization of the well-studied Set Cover problem (SC). In PSC the input consists of an integer $k$ and a set system $(U,S)$ where $U$ is a finite set, and $S \\subseteq 2^U$ is a collection of subsets of $U$. The goal is to find a subcollection $S' \\subseteq S$ of smallest cardinality such that sets in $S'$ cover at least $k$ elements of $U$; that is $|\\cup_{A \\in S'} A| \\ge k$. SC is a special case of PSC when $k = |U|$. In the weighted version each set $X \\in S$ has a non-negative weight $w(X)$ and the goal is to find a minimum weight subcollection to cover $k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04413","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"}