{"paper":{"title":"Deterministic $O(1)$-Approximation Algorithms to 1-Center Clustering with Outliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Shyam Narayanan","submitted_at":"2018-06-19T17:39:46Z","abstract_excerpt":"The 1-center clustering with outliers problem asks about identifying a prototypical robust statistic that approximates the location of a cluster of points. Given some constant $0 < \\alpha < 1$ and $n$ points such that $\\alpha n$ of them are in some (unknown) ball of radius $r,$ the goal is to compute a ball of radius $O(r)$ that also contains $\\alpha n$ points. This problem can be formulated with the points in a normed vector space such as $\\mathbb{R}^d$ or in a general metric space.\n  The problem has a simple randomized solution: a randomly selected point is a correct solution with constant p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07356","kind":"arxiv","version":2},"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"}