{"paper":{"title":"Super-fast MST Algorithms in the Congested Clique using $o(m)$ Messages","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":"2016-10-12T23:10:04Z","abstract_excerpt":"In a sequence of recent results (PODC 2015 and PODC 2016), the running time of the fastest algorithm for the \\emph{minimum spanning tree (MST)} problem in the \\emph{Congested Clique} model was first improved to $O(\\log \\log \\log n)$ from $O(\\log \\log n)$ (Hegeman et al., PODC 2015) and then to $O(\\log^* n)$ (Ghaffari and Parter, PODC 2016). All of these algorithms use $\\Theta(n^2)$ messages independent of the number of edges in the input graph.\n  This paper positively answers a question raised in Hegeman et al., and presents the first \"super-fast\" MST algorithm with $o(m)$ message complexity f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03897","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"}