2026-07-23T01:41:59Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:9164 2024-03-06T10:43:31Z ddc:004 open_access

(Delta+1) Coloring in the Congested Clique Model Parter, Merav Distributed Graph Algorithms Coloring Congested Clique In this paper, we present improved algorithms for the (Delta+1) (vertex) coloring problem in the Congested Clique model of distributed computing. In this model, the input is a graph on n nodes, initially each node knows only its incident edges, and per round each two nodes can exchange O(log n) bits of information. Our key result is a randomized (Delta+1) vertex coloring algorithm that works in O(log log Delta * log^* Delta)-rounds. This is achieved by combining the recent breakthrough result of [Chang-Li-Pettie, STOC'18] in the {LOCAL} model and a degree reduction technique. We also get the following results with high probability: (1) (Delta+1)-coloring for Delta=O((n/log n)^{1-epsilon}) for any epsilon in (0,1), within O(log(1/epsilon)log^* Delta) rounds, and (2) (Delta+Delta^{1/2+o(1)})-coloring within O(log^* Delta) rounds. Turning to deterministic algorithms, we show a (Delta+1)-coloring algorithm that works in O(log Delta) rounds. Our new bounds provide exponential improvements over the state of the art. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Merav Parter 2018 Is Part Of LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2018.160 urn:nbn:de:0030-drops-91640 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.160 eng https://creativecommons.org/licenses/by/3.0/legalcode