{"paper":{"title":"Output sensitive algorithm for covering many points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Hossein Ghasemalizadeh, Mohammadreza Razzazi","submitted_at":"2013-12-02T09:46:22Z","abstract_excerpt":"A set of points and a positive integer $m$ are given and our goal is to cover the maximum number of these point with $m$ disks. We devise the first output sensitive algorithm for this problem. We introduce a parameter $\\rho$ as the maximum number of points that one disk can cover. In this paper first we solve the problem for $m=2$ in $O({n\\rho} + {\\rho ^3}\\log \\rho ))$ time. The previous algorithm for this problem runs in $O({n^3}\\log n)$ time. Our algorithm outperforms the previous algorithm because $\\rho$ is much smaller than $n$ in many cases. Then we extend the algorithm for any value of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0389","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"}