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oai:drops-oai.dagstuhl.de:12883 2024-03-06T09:50:59Z ddc:004 open_access

An Optimal Decentralized (Δ + 1)-Coloring Algorithm Bertschinger, Daniel Lengler, Johannes Martinsson, Anders Meier, Robert Steger, Angelika Trujić, Miloš Welzl, Emo Decentralized Algorithm Distributed Computing Graph Coloring Randomized Algorithms Consider the following simple coloring algorithm for a graph on n vertices. Each vertex chooses a color from {1, ..., Δ(G) + 1} uniformly at random. While there exists a conflicted vertex choose one such vertex uniformly at random and recolor it with a randomly chosen color. This algorithm was introduced by Bhartia et al. [MOBIHOC'16] for channel selection in WIFI-networks. We show that this algorithm always converges to a proper coloring in expected O(n log Δ) steps, which is optimal and proves a conjecture of Chakrabarty and de Supinski [SOSA'20]. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Daniel Bertschinger and Johannes Lengler and Anders Martinsson and Robert Meier and Angelika Steger and Miloš Trujić and Emo Welzl 2020 Is Part Of LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2020.17 urn:nbn:de:0030-drops-128837 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.17 eng https://creativecommons.org/licenses/by/3.0/legalcode