{"paper":{"title":"A Las Vegas approximation algorithm for metric $1$-median selection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ching-Lueh Chang","submitted_at":"2017-02-10T09:11:18Z","abstract_excerpt":"Given an $n$-point metric space, consider the problem of finding a point with the minimum sum of distances to all points. We show that this problem has a randomized algorithm that {\\em always} outputs a $(2+\\epsilon)$-approximate solution in an expected $O(n/\\epsilon^2)$ time for each constant $\\epsilon>0$. Inheriting Indyk's algorithm, our algorithm outputs a $(1+\\epsilon)$-approximate $1$-median in $O(n/\\epsilon^2)$ time with probability $\\Omega(1)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03106","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"}