{"title":"s-Club聚类边删除问题的参数化复杂度","authors":"Fabrizio Montecchiani, Giacomo Ortali, Tommaso Piselli, Alessandra Tappini","doi":"10.48550/arXiv.2205.10834","DOIUrl":null,"url":null,"abstract":"We study the parameterized complexity of the $s$-Club Cluster Edge Deletion problem: Given a graph $G$ and two integers $s \\ge 2$ and $k \\ge 1$, is it possible to remove at most $k$ edges from $G$ such that each connected component of the resulting graph has diameter at most $s$? This problem is known to be NP-hard already when $s = 2$. We prove that it admits a fixed-parameter tractable algorithm when parameterized by $s$ and the treewidth of the input graph.","PeriodicalId":212849,"journal":{"name":"Italian Conference on Theoretical Computer Science","volume":"13 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Parametrized Complexity of the s-Club Cluster Edge Deletion Problem\",\"authors\":\"Fabrizio Montecchiani, Giacomo Ortali, Tommaso Piselli, Alessandra Tappini\",\"doi\":\"10.48550/arXiv.2205.10834\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the parameterized complexity of the $s$-Club Cluster Edge Deletion problem: Given a graph $G$ and two integers $s \\\\ge 2$ and $k \\\\ge 1$, is it possible to remove at most $k$ edges from $G$ such that each connected component of the resulting graph has diameter at most $s$? This problem is known to be NP-hard already when $s = 2$. We prove that it admits a fixed-parameter tractable algorithm when parameterized by $s$ and the treewidth of the input graph.\",\"PeriodicalId\":212849,\"journal\":{\"name\":\"Italian Conference on Theoretical Computer Science\",\"volume\":\"13 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-05-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Italian Conference on Theoretical Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48550/arXiv.2205.10834\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Italian Conference on Theoretical Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2205.10834","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the Parametrized Complexity of the s-Club Cluster Edge Deletion Problem
We study the parameterized complexity of the $s$-Club Cluster Edge Deletion problem: Given a graph $G$ and two integers $s \ge 2$ and $k \ge 1$, is it possible to remove at most $k$ edges from $G$ such that each connected component of the resulting graph has diameter at most $s$? This problem is known to be NP-hard already when $s = 2$. We prove that it admits a fixed-parameter tractable algorithm when parameterized by $s$ and the treewidth of the input graph.
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