{"paper":{"title":"Distributed Selection in $O ( \\log n )$ Time with $O ( n \\log \\log n )$ Messages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Junichiro Fukuyama, Piotr Berman","submitted_at":"2015-11-02T21:30:12Z","abstract_excerpt":"We consider the selection problem on a completely connected network of $n$ processors with no shared memory. Each processor initially holds a given numeric item of $b$ bits allowed to send a message of $\\max ( b, \\lg n )$ bits to another processor at a time. On such a communication network ${\\cal G}$, we show that the $k$th smallest of the $n$ inputs can be detected in $O ( \\log n )$ time with $O ( n \\log \\log n )$ messages. The possibility of such a parallel algorithm for this distributed $k$-selection problem has been unknown despite the intensive investigation on many variations of the sele"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00715","kind":"arxiv","version":4},"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"}