{"title":"γ 聚类问题:经典复杂性和参数复杂性","authors":"","doi":"10.1016/j.tcs.2024.114784","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce the <em>γ</em>-clustering problems, which are variants of the well-known <span>Cluster Editing/Deletion/Completion</span> problems, and defined as: given a graph <em>G</em>, how many edges must be edited in <em>G</em>, deleted from <em>G</em>, or added to <em>G</em> in order to have a disjoint union of <em>γ</em>-quasi-cliques. We provide here the complete complexity classification of these problems along with <span>FPT</span> algorithms parameterized by the number of modifications, for the <span>NP</span>-complete problems. We also study here a variant of these problems where the number of final clusters is a fixed constant, obtaining mostly the same results regarding classical and parameterized complexity.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304397524004018/pdfft?md5=d20acc68ac14e652d54dc6b5298c7c89&pid=1-s2.0-S0304397524004018-main.pdf","citationCount":"0","resultStr":"{\"title\":\"γ-clustering problems: Classical and parametrized complexity\",\"authors\":\"\",\"doi\":\"10.1016/j.tcs.2024.114784\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We introduce the <em>γ</em>-clustering problems, which are variants of the well-known <span>Cluster Editing/Deletion/Completion</span> problems, and defined as: given a graph <em>G</em>, how many edges must be edited in <em>G</em>, deleted from <em>G</em>, or added to <em>G</em> in order to have a disjoint union of <em>γ</em>-quasi-cliques. We provide here the complete complexity classification of these problems along with <span>FPT</span> algorithms parameterized by the number of modifications, for the <span>NP</span>-complete problems. We also study here a variant of these problems where the number of final clusters is a fixed constant, obtaining mostly the same results regarding classical and parameterized complexity.</p></div>\",\"PeriodicalId\":49438,\"journal\":{\"name\":\"Theoretical Computer Science\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-08-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0304397524004018/pdfft?md5=d20acc68ac14e652d54dc6b5298c7c89&pid=1-s2.0-S0304397524004018-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical Computer Science\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0304397524004018\",\"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/S0304397524004018","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
摘要
我们引入了 γ 聚类问题,它是众所周知的聚类编辑/删除/补全问题的变体,定义为:给定一个图 G,必须在 G 中编辑多少条边、从 G 中删除多少条边或向 G 中添加多少条边,才能得到一个 γ 准聚类的不相交联盟。我们在此提供了这些问题的完整复杂度分类,以及针对 NP-完全问题的、以修改数量为参数的 FPT 算法。我们还研究了这些问题的一个变体,即最终簇的数量是一个固定常数,在经典复杂度和参数化复杂度方面得到了大致相同的结果。
γ-clustering problems: Classical and parametrized complexity
We introduce the γ-clustering problems, which are variants of the well-known Cluster Editing/Deletion/Completion problems, and defined as: given a graph G, how many edges must be edited in G, deleted from G, or added to G in order to have a disjoint union of γ-quasi-cliques. We provide here the complete complexity classification of these problems along with FPT algorithms parameterized by the number of modifications, for the NP-complete problems. We also study here a variant of these problems where the number of final clusters is a fixed constant, obtaining mostly the same results regarding classical and parameterized complexity.
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.