期刊
DISCRETE APPLIED MATHEMATICS
卷 144, 期 1-2, 页码 173-182出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.dam.2004.01.007
关键词
clustering; cluster graph; graph modification problem; complexity; approximation
In a clustering problem one has to partition a set of elements into homogeneous and well-separated subsets. From a graph theoretic point of view, a cluster graph is a vertex-disjoint union of cliques. The clustering problem is the task of making the fewest changes to the edge set of an input graph so that it becomes a cluster graph. We study the complexity of three variants of the problem. In the Cluster Completion variant edges can only be added. In Cluster Deletion, edges can only be deleted. In Cluster Editing, both edge additions and edge deletions are allowed. We also study these variants when the desired solution must contain a prespecified number of clusters. We show that Cluster Editing is NP-complete, Cluster Deletion is NP-hard to approximate to within some constant factor, and Cluster Completion is polynomial. When the desired solution must contain exactly p clusters, we show that Cluster Editing is NP-complete for every p greater than or equal to 2; Cluster Deletion is polynomial for p = 2 but NP-complete for p > 2; and Cluster Completion is polynomial for any p. We also give a constant factor approximation algorithm for a variant of Cluster Editing when p = 2. (C) 2004 Elsevier B.V. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据