{"paper":{"title":"Minimum-weight Spanning Tree Construction in $O(\\log \\log \\log n)$ Rounds on the Congested Clique","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DC","authors_text":"Sriram V. Pemmaraju, Vivek B. Sardeshmukh","submitted_at":"2014-12-07T09:29:42Z","abstract_excerpt":"This paper considers the \\textit{minimum spanning tree (MST)} problem in the Congested Clique model and presents an algorithm that runs in $O(\\log \\log \\log n)$ rounds, with high probability. Prior to this, the fastest MST algorithm in this model was a deterministic algorithm due to Lotker et al.~(SIAM J on Comp, 2005) from about a decade ago. A key step along the way to designing this MST algorithm is a \\textit{connectivity verification} algorithm that not only runs in $O(\\log \\log \\log n)$ rounds with high probability, but also has low message complexity. This allows the fast computation of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2333","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"}