{"paper":{"title":"Unique Set Cover on Unit Disks and Unit Squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Saeed Mehrabi","submitted_at":"2016-07-25T17:38:39Z","abstract_excerpt":"We study the Unique Set Cover problem on unit disks and unit squares. For a given set $P$ of $n$ points and a set $D$ of $m$ geometric objects both in the plane, the objective of the Unique Set Cover problem is to select a subset $D'\\subseteq D$ of objects such that every point in $P$ is covered by at least one object in $D'$ and the number of points covered uniquely is maximized, where a point is covered uniquely if the point is covered by exactly one object in $D'$. In this paper, (i) we show that the Unique Set Cover is NP-hard on both unit disks and unit squares, and (ii) we give a PTAS fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07378","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"}