{"title":"f 匹配的分布式近似法","authors":"","doi":"10.1016/j.tcs.2024.114760","DOIUrl":null,"url":null,"abstract":"<div><p>Let <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> be a graph and let <span><math><mi>f</mi><mo>:</mo><mi>V</mi><mo>→</mo><msup><mrow><mi>Z</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>. An <em>f</em>-matching in <em>G</em> is a set of edges <span><math><mi>F</mi><mo>⊆</mo><mi>E</mi></math></span> such that every vertex <span><math><mi>v</mi><mo>∈</mo><mi>V</mi></math></span> is incident to at most <span><math><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo></math></span> edges. In this paper we will give a constant-time distributed algorithm which approximates a maximum <em>f</em>-matching in bi-colored graphs of constant arboricity.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Distributed approximation for f-matching\",\"authors\":\"\",\"doi\":\"10.1016/j.tcs.2024.114760\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> be a graph and let <span><math><mi>f</mi><mo>:</mo><mi>V</mi><mo>→</mo><msup><mrow><mi>Z</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>. An <em>f</em>-matching in <em>G</em> is a set of edges <span><math><mi>F</mi><mo>⊆</mo><mi>E</mi></math></span> such that every vertex <span><math><mi>v</mi><mo>∈</mo><mi>V</mi></math></span> is incident to at most <span><math><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo></math></span> edges. In this paper we will give a constant-time distributed algorithm which approximates a maximum <em>f</em>-matching in bi-colored graphs of constant arboricity.</p></div>\",\"PeriodicalId\":49438,\"journal\":{\"name\":\"Theoretical Computer Science\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-07-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical Computer Science\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0304397524003773\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Computer Science","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304397524003773","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}
Let be a graph and let . An f-matching in G is a set of edges such that every vertex is incident to at most edges. In this paper we will give a constant-time distributed algorithm which approximates a maximum f-matching in bi-colored graphs of constant arboricity.
期刊介绍:
Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.