{"paper":{"title":"On Partial Covering For Geometric Set Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Kasturi Varadarajan, Tanmay Inamdar","submitted_at":"2017-11-13T22:50:49Z","abstract_excerpt":"We study a generalization of the Set Cover problem called the \\emph{Partial Set Cover} in the context of geometric set systems. The input to this problem is a set system $(X, \\mathcal{S})$, where $X$ is a set of elements and $\\mathcal{S}$ is a collection of subsets of $X$, and an integer $k \\le |X|$. The goal is to cover at least $k$ elements of $X$ by using a minimum-weight collection of sets from $\\mathcal{S}$. The main result of this article is an LP rounding scheme which shows that the integrality gap of the Partial Set Cover LP is at most a constant times that of the Set Cover LP for a ce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04882","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"}