{"paper":{"title":"Metric 1-median selection with fewer queries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ching-Lueh Chang","submitted_at":"2016-12-27T15:19:59Z","abstract_excerpt":"Let $h\\colon\\mathbb{Z}^+\\to\\mathbb{Z}^+\\setminus\\{1\\}$ be any function such that $h(n)$ and $\\lceil n^{1/h(n)}\\rceil$ are computable from $n$ in $O(h(n)\\cdot n^{1+1/h(n)})$ time. We show that given any $n$-point metric space $(M,d)$, the problem of finding $\\mathop{\\mathrm{argmin}}_{i\\in M}\\,\\sum_{j\\in M}\\,d(i,j)$ (breaking ties arbitrarily) has a deterministic, $O(h(n)\\cdot n^{1+1/h(n)})$-time, $O(n^{1+1/h(n)})$-query, $(2\\,h(n))$-approximation and nonadaptive algorithm. Our proofs modify those of Chang~\\cite{Cha15, Cha15CMCT} with the following improvements: (1) We improve Chang's~\\cite{Cha1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08654","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"}