{"paper":{"title":"Approximating $k$-Median via Pseudo-Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ola Svensson, Shi Li","submitted_at":"2012-11-01T18:02:58Z","abstract_excerpt":"We present a novel approximation algorithm for $k$-median that achieves an approximation guarantee of\n  $1+\\sqrt{3}+\\epsilon$, improving upon the decade-old ratio of $3+\\epsilon$. Our approach is based on two components, each of which, we believe, is of independent interest.\n  First, we show that in order to give an $\\alpha$-approximation algorithm for $k$-median, it is sufficient to give a \\emph{pseudo-approximation algorithm} that finds an $\\alpha$-approximate solution by opening $k+O(1)$ facilities. This is a rather surprising result as there exist instances for which opening $k+1$ faciliti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0243","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"}