{"paper":{"title":"Hardness of Approximation of Euclidean $k$-Median","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.DS","cs.LG"],"primary_cat":"cs.CC","authors_text":"Anup Bhattacharya, Dishant Goyal, Ragesh Jaiswal","submitted_at":"2020-11-09T06:50:34Z","abstract_excerpt":"The Euclidean $k$-median problem is defined in the following manner: given a set $\\mathcal{X}$ of $n$ points in $\\mathbb{R}^{d}$, and an integer $k$, find a set $C \\subset \\mathbb{R}^{d}$ of $k$ points (called centers) such that the cost function $\\Phi(C,\\mathcal{X}) \\equiv \\sum_{x \\in \\mathcal{X}} \\min_{c \\in C} \\|x-c\\|_{2}$ is minimized. The Euclidean $k$-means problem is defined similarly by replacing the distance with squared distance in the cost function. Various hardness of approximation results are known for the Euclidean $k$-means problem. However, no hardness of approximation results "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.04221","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.04221/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}