{"paper":{"title":"Approximate Clustering via Metric Partitioning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.PR"],"primary_cat":"cs.CG","authors_text":"Kasturi Varadarajan, Sayan Bandyapadhyay","submitted_at":"2015-07-08T17:08:13Z","abstract_excerpt":"In this paper we consider two metric covering/clustering problems - \\textit{Minimum Cost Covering Problem} (MCC) and $k$-clustering. In the MCC problem, we are given two point sets $X$ (clients) and $Y$ (servers), and a metric on $X \\cup Y$. We would like to cover the clients by balls centered at the servers. The objective function to minimize is the sum of the $\\alpha$-th power of the radii of the balls. Here $\\alpha \\geq 1$ is a parameter of the problem (but not of a problem instance). MCC is closely related to the $k$-clustering problem. The main difference between $k$-clustering and MCC is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02222","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"}