{"title":"Some graph partitioning problems and algorithms related to routing in large computer networks","authors":"A. Bouloutas, P. Gopal","doi":"10.1109/ICDCS.1989.37966","DOIUrl":null,"url":null,"abstract":"The problem of partitioning a large computer network into clusters in order to reduce the amount of network resources consumed by the routing algorithm is addressed. The clustering problem is formulated as a general graph partitioning problem. It is shown that the problem of partitioning a graph into a minimum number of clusters with unit weight vertices and a given weight bound on the cluster size is NP-complete if each cluster is required to be internally connected. It is also shown that if a diameter bound is imposed on the cluster instead of the weight bound, then the problem is NP-complete, even when cluster connectivity is not required. An optimum partitioning algorithm is presented for the latter problem when the graph is a tree. An optimum partitioning algorithm is presented for another problem in which each cluster is required to contain exactly one of a set of specified vertices called cluster heads.<<ETX>>","PeriodicalId":266544,"journal":{"name":"[1989] Proceedings. The 9th International Conference on Distributed Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1989-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1989] Proceedings. The 9th International Conference on Distributed Computing Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICDCS.1989.37966","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 11
Abstract
The problem of partitioning a large computer network into clusters in order to reduce the amount of network resources consumed by the routing algorithm is addressed. The clustering problem is formulated as a general graph partitioning problem. It is shown that the problem of partitioning a graph into a minimum number of clusters with unit weight vertices and a given weight bound on the cluster size is NP-complete if each cluster is required to be internally connected. It is also shown that if a diameter bound is imposed on the cluster instead of the weight bound, then the problem is NP-complete, even when cluster connectivity is not required. An optimum partitioning algorithm is presented for the latter problem when the graph is a tree. An optimum partitioning algorithm is presented for another problem in which each cluster is required to contain exactly one of a set of specified vertices called cluster heads.<>