{"paper":{"title":"Fast Approximation and Randomized Algorithms for Diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Bahman Kalantari, Hamid Homapour, Sharareh Alipour","submitted_at":"2014-10-08T17:41:19Z","abstract_excerpt":"We consider approximation of diameter of a set $S$ of $n$ points in dimension $m$. E$\\tilde{g}$ecio$\\tilde{g}$lu and Kalantari \\cite{kal} have shown that given any $p \\in S$, by computing its farthest in $S$, say $q$, and in turn the farthest point of $q$, say $q'$, we have ${\\rm diam}(S) \\leq \\sqrt{3} d(q,q')$. Furthermore, iteratively replacing $p$ with an appropriately selected point on the line segment $pq$, in at most $t \\leq n$ additional iterations, the constant bound factor is improved to $c_*=\\sqrt{5-2\\sqrt{3}} \\approx 1.24$. Here we prove when $m=2$, $t=1$. This suggests in practice "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2195","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"}