{"paper":{"title":"Metric random matchings with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ching-Lueh Chang","submitted_at":"2017-03-24T14:44:04Z","abstract_excerpt":"Let $(\\{1,2,\\ldots,n\\},d)$ be a metric space. We analyze the expected value and the variance of $\\sum_{i=1}^{\\lfloor n/2\\rfloor}\\,d({\\boldsymbol{\\pi}}(2i-1),{\\boldsymbol{\\pi}}(2i))$ for a uniformly random permutation ${\\boldsymbol{\\pi}}$ of $\\{1,2,\\ldots,n\\}$, leading to the following results: (I) Consider the problem of finding a point in $\\{1,2,\\ldots,n\\}$ with the minimum sum of distances to all points. We show that this problem has a randomized algorithm that (1) always outputs a $(2+\\epsilon)$-approximate solution in expected $O(n/\\epsilon^2)$ time and that (2) inherits Indyk's~\\cite{Ind9"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08433","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"}