{"title":"不一致的派系问题","authors":"K. Jansen, Petra Scheffler, G. Woeginger","doi":"10.1051/RO/1997310100451","DOIUrl":null,"url":null,"abstract":"Given a graph G = (V, E), we consider the problem of finding a set of D pairwise disjoint cliques in the graph with maximum overall number of vertices. We determine the computational complexity of this problem restricted to a variety of different graph classes. We give polynomial time algorithms for the problem restricted to interval graphs, cographs, directed path graphs and partial k-trees. In contrast, we show the NP-completeness of this problem for undirected path graphs. Moreover, we investigate a closely related scheduling problem. Given D times units, we look for a sequence of workers w 1 ,...,w K and a partition J 1 ,..., J k of the job set such that J i can be executed by w i within D time units. The goal is to find a sequence with minimum total wage of the workers.","PeriodicalId":142744,"journal":{"name":"Universität Trier, Mathematik/Informatik, Forschungsbericht","volume":"80 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"21","resultStr":"{\"title\":\"The Disjoint Cliques Problem\",\"authors\":\"K. Jansen, Petra Scheffler, G. Woeginger\",\"doi\":\"10.1051/RO/1997310100451\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given a graph G = (V, E), we consider the problem of finding a set of D pairwise disjoint cliques in the graph with maximum overall number of vertices. We determine the computational complexity of this problem restricted to a variety of different graph classes. We give polynomial time algorithms for the problem restricted to interval graphs, cographs, directed path graphs and partial k-trees. In contrast, we show the NP-completeness of this problem for undirected path graphs. Moreover, we investigate a closely related scheduling problem. Given D times units, we look for a sequence of workers w 1 ,...,w K and a partition J 1 ,..., J k of the job set such that J i can be executed by w i within D time units. The goal is to find a sequence with minimum total wage of the workers.\",\"PeriodicalId\":142744,\"journal\":{\"name\":\"Universität Trier, Mathematik/Informatik, Forschungsbericht\",\"volume\":\"80 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"21\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Universität Trier, Mathematik/Informatik, Forschungsbericht\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1051/RO/1997310100451\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Universität Trier, Mathematik/Informatik, Forschungsbericht","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/RO/1997310100451","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Given a graph G = (V, E), we consider the problem of finding a set of D pairwise disjoint cliques in the graph with maximum overall number of vertices. We determine the computational complexity of this problem restricted to a variety of different graph classes. We give polynomial time algorithms for the problem restricted to interval graphs, cographs, directed path graphs and partial k-trees. In contrast, we show the NP-completeness of this problem for undirected path graphs. Moreover, we investigate a closely related scheduling problem. Given D times units, we look for a sequence of workers w 1 ,...,w K and a partition J 1 ,..., J k of the job set such that J i can be executed by w i within D time units. The goal is to find a sequence with minimum total wage of the workers.