{"paper":{"title":"Dispersion in disks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CG","authors_text":"Adrian Dumitrescu, Minghui Jiang","submitted_at":"2009-12-11T01:09:55Z","abstract_excerpt":"We present three new approximation algorithms with improved constant ratios for selecting $n$ points in $n$ disks such that the minimum pairwise distance among the points is maximized.\n  (1) A very simple $O(n\\log n)$-time algorithm with ratio $0.511$ for disjoint unit disks.\n  (2) An LP-based algorithm with ratio $0.707$ for disjoint disks of arbitrary radii that uses a linear number of variables and constraints, and runs in polynomial time.\n  (3) A hybrid algorithm with ratio either $0.4487$ or $0.4674$ for (not necessarily disjoint) unit disks that uses an algorithm of Cabello in combinatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2125","kind":"arxiv","version":3},"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"}