在不学习邻居颜色的情况下快速着色

Proceedings of the ... International Symposium on High Performance Distributed Computing Pub Date : 2020-08-10 DOI:10.4230/LIPIcs.DISC.2020.39

M. Halldórsson, F. Kuhn, Yannic Maus, Alexandre Nolin

{"title":"在不学习邻居颜色的情况下快速着色","authors":"M. Halldórsson, F. Kuhn, Yannic Maus, Alexandre Nolin","doi":"10.4230/LIPIcs.DISC.2020.39","DOIUrl":null,"url":null,"abstract":"We give an improved randomized CONGEST algorithm for distance-$2$ coloring that uses $\\Delta^2+1$ colors and runs in $O(\\log n)$ rounds, improving the recent $O(\\log \\Delta \\cdot \\log n)$-round algorithm in [Halldorsson, Kuhn, Maus; PODC '20]. We then improve the time complexity to $O(\\log \\Delta) + 2^{O(\\sqrt{\\log\\log n})}$.","PeriodicalId":89463,"journal":{"name":"Proceedings of the ... International Symposium on High Performance Distributed Computing","volume":"22 1","pages":"39:1-39:17"},"PeriodicalIF":0.0000,"publicationDate":"2020-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Coloring Fast Without Learning Your Neighbors' Colors\",\"authors\":\"M. Halldórsson, F. Kuhn, Yannic Maus, Alexandre Nolin\",\"doi\":\"10.4230/LIPIcs.DISC.2020.39\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give an improved randomized CONGEST algorithm for distance-$2$ coloring that uses $\\\\Delta^2+1$ colors and runs in $O(\\\\log n)$ rounds, improving the recent $O(\\\\log \\\\Delta \\\\cdot \\\\log n)$-round algorithm in [Halldorsson, Kuhn, Maus; PODC '20]. We then improve the time complexity to $O(\\\\log \\\\Delta) + 2^{O(\\\\sqrt{\\\\log\\\\log n})}$.\",\"PeriodicalId\":89463,\"journal\":{\"name\":\"Proceedings of the ... International Symposium on High Performance Distributed Computing\",\"volume\":\"22 1\",\"pages\":\"39:1-39:17\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-08-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the ... International Symposium on High Performance Distributed Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.DISC.2020.39\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the ... International Symposium on High Performance Distributed Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/LIPIcs.DISC.2020.39","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 9

摘要

给出了一种改进的距离-随机化拥塞算法$2$ 使用的着色 $\Delta^2+1$ 颜色和颜色 $O(\log n)$ 回合，近期有所改善 $O(\log \Delta \cdot \log n)$-round算法[Halldorsson, Kuhn, Maus;][20]。然后我们将时间复杂度提高到 $O(\log \Delta) + 2^{O(\sqrt{\log\log n})}$．

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Coloring Fast Without Learning Your Neighbors' Colors

We give an improved randomized CONGEST algorithm for distance-$2$ coloring that uses $\Delta^2+1$ colors and runs in $O(\log n)$ rounds, improving the recent $O(\log \Delta \cdot \log n)$-round algorithm in [Halldorsson, Kuhn, Maus; PODC '20]. We then improve the time complexity to $O(\log \Delta) + 2^{O(\sqrt{\log\log n})}$.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Proceedings of the ... International Symposium on High Performance Distributed Computing

自引率

0.00%

发文量