改进的分布式Δ -着色。

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Distributed Computing Pub Date : 2021-01-01 Epub Date: 2021-07-09 DOI:10.1007/s00446-021-00397-4

Mohsen Ghaffari, Juho Hirvonen, Fabian Kuhn, Yannic Maus

{"title":"改进的分布式Δ -着色。","authors":"Mohsen Ghaffari, Juho Hirvonen, Fabian Kuhn, Yannic Maus","doi":"10.1007/s00446-021-00397-4","DOIUrl":null,"url":null,"abstract":"We present a randomized distributed algorithm that computes a <math><mi>Δ</mi></math> -coloring in any non-complete graph with maximum degree <math><mrow><mi>Δ</mi> <mo>≥</mo> <mn>4</mn></mrow> </math> in <math><mrow><mi>O</mi> <mrow><mo>(</mo> <mo>log</mo> <mi>Δ</mi> <mo>)</mo></mrow> <mo>+</mo> <msup><mn>2</mn> <mrow><mi>O</mi> <mo>(</mo> <msqrt><mrow><mo>log</mo> <mo>log</mo> <mi>n</mi></mrow> </msqrt> <mo>)</mo></mrow> </msup> </mrow> </math> rounds, as well as a randomized algorithm that computes a <math><mi>Δ</mi></math> -coloring in <math><mrow><mi>O</mi> <mo>(</mo> <msup><mrow><mo>(</mo> <mo>log</mo> <mo>log</mo> <mi>n</mi> <mo>)</mo></mrow> <mn>2</mn></msup> <mo>)</mo></mrow> </math> rounds when <math><mrow><mi>Δ</mi> <mo>∈</mo> <mo>[</mo> <mn>3</mn> <mo>,</mo> <mi>O</mi> <mo>(</mo> <mn>1</mn> <mo>)</mo> <mo>]</mo></mrow> </math> . Both these algorithms improve on an <math><mrow><mi>O</mi> <mo>(</mo> <msup><mo>log</mo> <mn>3</mn></msup> <mi>n</mi> <mo>/</mo> <mo>log</mo> <mi>Δ</mi> <mo>)</mo></mrow> </math> -round algorithm of Panconesi and Srinivasan (STOC'93), which has remained the state of the art for the past 25 years. Moreover, the latter algorithm gets (exponentially) closer to an <math><mrow><mi>Ω</mi> <mo>(</mo> <mo>log</mo> <mo>log</mo> <mi>n</mi> <mo>)</mo></mrow> </math> round lower bound of Brandt et al. (STOC'16).","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"34 4","pages":"239-258"},"PeriodicalIF":1.3000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00446-021-00397-4","citationCount":"13","resultStr":"{\"title\":\"<ArticleTitle xmlns:ns0=\\\"http://www.w3.org/1998/Math/MathML\\\">Improved distributed <ns0:math><ns0:mi>Δ</ns0:mi></ns0:math> -coloring.\",\"authors\":\"Mohsen Ghaffari, Juho Hirvonen, Fabian Kuhn, Yannic Maus\",\"doi\":\"10.1007/s00446-021-00397-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a randomized distributed algorithm that computes a <math><mi>Δ</mi></math> -coloring in any non-complete graph with maximum degree <math><mrow><mi>Δ</mi> <mo>≥</mo> <mn>4</mn></mrow> </math> in <math><mrow><mi>O</mi> <mrow><mo>(</mo> <mo>log</mo> <mi>Δ</mi> <mo>)</mo></mrow> <mo>+</mo> <msup><mn>2</mn> <mrow><mi>O</mi> <mo>(</mo> <msqrt><mrow><mo>log</mo> <mo>log</mo> <mi>n</mi></mrow> </msqrt> <mo>)</mo></mrow> </msup> </mrow> </math> rounds, as well as a randomized algorithm that computes a <math><mi>Δ</mi></math> -coloring in <math><mrow><mi>O</mi> <mo>(</mo> <msup><mrow><mo>(</mo> <mo>log</mo> <mo>log</mo> <mi>n</mi> <mo>)</mo></mrow> <mn>2</mn></msup> <mo>)</mo></mrow> </math> rounds when <math><mrow><mi>Δ</mi> <mo>∈</mo> <mo>[</mo> <mn>3</mn> <mo>,</mo> <mi>O</mi> <mo>(</mo> <mn>1</mn> <mo>)</mo> <mo>]</mo></mrow> </math> . Both these algorithms improve on an <math><mrow><mi>O</mi> <mo>(</mo> <msup><mo>log</mo> <mn>3</mn></msup> <mi>n</mi> <mo>/</mo> <mo>log</mo> <mi>Δ</mi> <mo>)</mo></mrow> </math> -round algorithm of Panconesi and Srinivasan (STOC'93), which has remained the state of the art for the past 25 years. Moreover, the latter algorithm gets (exponentially) closer to an <math><mrow><mi>Ω</mi> <mo>(</mo> <mo>log</mo> <mo>log</mo> <mi>n</mi> <mo>)</mo></mrow> </math> round lower bound of Brandt et al. (STOC'16).\",\"PeriodicalId\":50569,\"journal\":{\"name\":\"Distributed Computing\",\"volume\":\"34 4\",\"pages\":\"239-258\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s00446-021-00397-4\",\"citationCount\":\"13\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Distributed Computing\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1007/s00446-021-00397-4\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2021/7/9 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Distributed Computing","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s00446-021-00397-4","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2021/7/9 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}

引用次数: 13

摘要

我们提出了一种随机分布算法，该算法在O (log Δ) + 2 O (log log n)轮中计算最大度Δ≥4的任何非完全图的Δ -着色，以及当Δ∈[3,o(1)]时，在O ((log log n) 2)轮中计算Δ -着色。这两种算法都改进了Panconesi和Srinivasan (STOC'93)的O (log 3 n / log Δ)轮算法，该算法在过去25年中一直保持着最先进的水平。此外，后一种算法(指数地)更接近于Brandt等人(STOC'16)的Ω (log log n)圆下界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

<ArticleTitle xmlns:ns0="http://www.w3.org/1998/Math/MathML">Improved distributed <ns0:math><ns0:mi>Δ</ns0:mi></ns0:math> -coloring.

查看原文本刊更多论文

Improved distributed Δ -coloring.

We present a randomized distributed algorithm that computes a $Δ$ -coloring in any non-complete graph with maximum degree $Δ \geq 4$ in $O (log Δ) + 2^{O (\sqrt{log log n})}$ rounds, as well as a randomized algorithm that computes a $Δ$ -coloring in $O ({(log log n)}^{2})$ rounds when $Δ \in [3, O (1)]$ . Both these algorithms improve on an $O ({log}^{3} n / log Δ)$ -round algorithm of Panconesi and Srinivasan (STOC'93), which has remained the state of the art for the past 25 years. Moreover, the latter algorithm gets (exponentially) closer to an $Ω (log log n)$ round lower bound of Brandt et al. (STOC'16).

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

Distributed Computing 工程技术-计算机：理论方法

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The international journal Distributed Computing provides a forum for original and significant contributions to the theory, design, specification and implementation of distributed systems. Topics covered by the journal include but are not limited to: design and analysis of distributed algorithms; multiprocessor and multi-core architectures and algorithms; synchronization protocols and concurrent programming; distributed operating systems and middleware; fault-tolerance, reliability and availability; architectures and protocols for communication networks and peer-to-peer systems; security in distributed computing, cryptographic protocols; mobile, sensor, and ad hoc networks; internet applications; concurrency theory; specification, semantics, verification, and testing of distributed systems. In general, only original papers will be considered. By virtue of submitting a manuscript to the journal, the authors attest that it has not been published or submitted simultaneously for publication elsewhere. However, papers previously presented in conference proceedings may be submitted in enhanced form. If a paper has appeared previously, in any form, the authors must clearly indicate this and provide an account of the differences between the previously appeared form and the submission.