{"paper":{"title":"Fast Clustering with Lower Bounds: No Customer too Far, No Shop too Small","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Alina Ene, Benjamin Raichel, Sariel Har-Peled","submitted_at":"2013-04-27T02:36:20Z","abstract_excerpt":"We study the \\LowerBoundedCenter (\\lbc) problem, which is a clustering problem that can be viewed as a variant of the \\kCenter problem. In the \\lbc problem, we are given a set of points P in a metric space and a lower bound \\lambda, and the goal is to select a set C \\subseteq P of centers and an assignment that maps each point in P to a center of C such that each center of C is assigned at least \\lambda points. The price of an assignment is the maximum distance between a point and the center it is assigned to, and the goal is to find a set of centers and an assignment of minimum price. We give"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7318","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"}