Cluster graph modification problems

Ron Shamir, Roded Sharan, Dekel Tsur

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

36 Scopus citations


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 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 NPhard 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 ≥ 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 Cluster Editing when p = 2.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 28th International Workshop, WG 2002, Revised Papers
EditorsLudek Kucera
PublisherSpringer Verlag
Number of pages12
ISBN (Print)3540003312, 9783540003311
StatePublished - 1 Jan 2002
Externally publishedYes
Event28th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2002 - Cesky Krumlov, Czech Republic
Duration: 13 Jun 200215 Jun 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2573 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference28th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2002
Country/TerritoryCzech Republic
CityCesky Krumlov

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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