{"paper":{"title":"Lessons from the Congested Clique Applied to MapReduce","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DC","authors_text":"James W. Hegeman, Sriram V. Pemmaraju","submitted_at":"2014-05-17T06:31:32Z","abstract_excerpt":"The main results of this paper are (I) a simulation algorithm which, under quite general constraints, transforms algorithms running on the Congested Clique into algorithms running in the MapReduce model, and (II) a distributed $O(\\Delta)$-coloring algorithm running on the Congested Clique which has an expected running time of (i) $O(1)$ rounds, if $\\Delta \\geq \\Theta(\\log^4 n)$; and (ii) $O(\\log \\log n)$ rounds otherwise. Applying the simulation theorem to the Congested-Clique $O(\\Delta)$-coloring algorithm yields an $O(1)$-round $O(\\Delta)$-coloring algorithm in the MapReduce model.\n  Our sim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4356","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"}