{"title":"分布(Δ +1)-次对数轮的着色","authors":"David G. Harris, Johannes Schneider, Hsin-Hao Su","doi":"10.1145/3178120","DOIUrl":null,"url":null,"abstract":"We give a new randomized distributed algorithm for (Δ +1)-coloring in the LOCAL model, running in O(√ log Δ)+ 2O(√log log n) rounds in a graph of maximum degree Δ. This implies that the (Δ +1)-coloring problem is easier than the maximal independent set problem and the maximal matching problem, due to their lower bounds of Ω(min(√/log n log log n, /log Δ log log Δ)) by Kuhn, Moscibroda, and Wattenhofer [PODC’04]. Our algorithm also extends to list-coloring where the palette of each node contains Δ +1 colors. We extend the set of distributed symmetry-breaking techniques by performing a decomposition of graphs into dense and sparse parts.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":"17 1","pages":"1 - 21"},"PeriodicalIF":0.0000,"publicationDate":"2018-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"28","resultStr":"{\"title\":\"Distributed (Δ +1)-Coloring in Sublogarithmic Rounds\",\"authors\":\"David G. Harris, Johannes Schneider, Hsin-Hao Su\",\"doi\":\"10.1145/3178120\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give a new randomized distributed algorithm for (Δ +1)-coloring in the LOCAL model, running in O(√ log Δ)+ 2O(√log log n) rounds in a graph of maximum degree Δ. This implies that the (Δ +1)-coloring problem is easier than the maximal independent set problem and the maximal matching problem, due to their lower bounds of Ω(min(√/log n log log n, /log Δ log log Δ)) by Kuhn, Moscibroda, and Wattenhofer [PODC’04]. Our algorithm also extends to list-coloring where the palette of each node contains Δ +1 colors. We extend the set of distributed symmetry-breaking techniques by performing a decomposition of graphs into dense and sparse parts.\",\"PeriodicalId\":17199,\"journal\":{\"name\":\"Journal of the ACM (JACM)\",\"volume\":\"17 1\",\"pages\":\"1 - 21\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-04-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"28\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the ACM (JACM)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3178120\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the ACM (JACM)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3178120","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Distributed (Δ +1)-Coloring in Sublogarithmic Rounds
We give a new randomized distributed algorithm for (Δ +1)-coloring in the LOCAL model, running in O(√ log Δ)+ 2O(√log log n) rounds in a graph of maximum degree Δ. This implies that the (Δ +1)-coloring problem is easier than the maximal independent set problem and the maximal matching problem, due to their lower bounds of Ω(min(√/log n log log n, /log Δ log log Δ)) by Kuhn, Moscibroda, and Wattenhofer [PODC’04]. Our algorithm also extends to list-coloring where the palette of each node contains Δ +1 colors. We extend the set of distributed symmetry-breaking techniques by performing a decomposition of graphs into dense and sparse parts.
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