{"paper":{"title":"Linear Time Approximation Schemes for Geometric Maximum Coverage","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Bowei Zhang, Haitao Wang, Jian Li, Kai Jin, Ningye Zhang","submitted_at":"2017-02-07T01:11:38Z","abstract_excerpt":"We study approximation algorithms for the following geometric version of the maximum coverage problem: Let $\\mathcal{P}$ be a set of $n$ weighted points in the plane. Let $D$ represent a planar object, such as a rectangle, or a disk. We want to place $m$ copies of $D$ such that the sum of the weights of the points in $\\mathcal{P}$ covered by these copies is maximized. For any fixed $\\varepsilon>0$, we present efficient approximation schemes that can find a $(1-\\varepsilon)$-approximation to the optimal solution. In particular, for $m=1$ and for the special case where $D$ is a rectangle, our al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01836","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"}