{"title":"Distributed fractional local ratio and independent set approximation","authors":"Magnús M. Halldórsson , Dror Rawitz","doi":"10.1016/j.ic.2024.105238","DOIUrl":null,"url":null,"abstract":"<div><div>We consider the <span>Maximum Weight Independent Set</span> problem, with a focus on obtaining good approximations for graphs of small maximum degree Δ. We give deterministic local algorithms running in time <span><math><mi>poly</mi><mo>(</mo><mi>Δ</mi><mo>,</mo><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span> that come close to matching the best centralized results known and improve the previous distributed approximations by a factor of about 2. More precisely, we obtain approximations below <span><math><mfrac><mrow><mi>Δ</mi><mo>+</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>, and a further improvement to <span><math><mn>8</mn><mo>/</mo><mn>5</mn><mo>+</mo><mi>ε</mi></math></span> when <span><math><mi>Δ</mi><mo>=</mo><mn>3</mn></math></span>.</div><div>Technically, this is achieved by leveraging the <em>fractional local ratio</em> technique, for a first application in a distributed setting.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"303 ","pages":"Article 105238"},"PeriodicalIF":0.8000,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Information and Computation","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0890540124001032","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the Maximum Weight Independent Set problem, with a focus on obtaining good approximations for graphs of small maximum degree Δ. We give deterministic local algorithms running in time that come close to matching the best centralized results known and improve the previous distributed approximations by a factor of about 2. More precisely, we obtain approximations below , and a further improvement to when .
Technically, this is achieved by leveraging the fractional local ratio technique, for a first application in a distributed setting.
期刊介绍：
Information and Computation welcomes original papers in all areas of theoretical computer science and computational applications of information theory. Survey articles of exceptional quality will also be considered. Particularly welcome are papers contributing new results in active theoretical areas such as
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Inductive inference and learning theory-
Logic & constraint programming-
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Symbolic computation, lambda calculus, and rewriting systems-
Types and typechecking
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