{"paper":{"title":"The Complexity of $(\\Delta + 1)$Coloring inCongested Clique, Massively Parallel Computation,and Centralized Local Computation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jara Uitto, Manuela Fischer, Mohsen Ghaffari, Yi-Jun Chang, Yufan Zheng","submitted_at":"2018-08-25T12:17:41Z","abstract_excerpt":"We present new randomized algorithms that improve the complexity of the classic $(\\Delta+1)$-coloring problem, and its generalization $(\\Delta+1)$-list-coloring, in three well-studied models of distributed, parallel, and centralized computation:\n  Distributed Congested Clique: We present an $O(1)$-round randomized algorithm for $(\\Delta+1)$-list coloring in the congested clique model of distributed computing. This settles the asymptotic complexity of this problem. It moreover improves upon the $O(\\log^\\ast \\Delta)$-round randomized algorithms of Parter and Su [DISC'18] and $O((\\log\\log \\Delta)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08419","kind":"arxiv","version":3},"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"}