Article

Cluster Graph Modification Problems

Authors:

Dekel TsurAuthors Info & Claims

WG '02: Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science

Pages 379 - 390

Published: 13 June 2002 Publication History

Abstract

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 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 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.

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Cited By

Bulhes Tde Sousa Filho GSubramanian ACabral L(2017)Branch-and-cut approaches for p-Cluster EditingDiscrete Applied Mathematics10.1016/j.dam.2016.10.026219:C(51-64)Online publication date: 11-Mar-2017
https://dl.acm.org/doi/10.1016/j.dam.2016.10.026
Bulhões TSubramanian ASousa Filho GCabral L(2017)Branch-and-price for p-cluster editingComputational Optimization and Applications10.1007/s10589-017-9893-x67:2(293-316)Online publication date: 1-Jun-2017
https://dl.acm.org/doi/10.1007/s10589-017-9893-x
Chen JMeng J(2010)A 2k Kernel for the cluster editing problemProceedings of the 16th annual international conference on Computing and combinatorics10.5555/1886811.1886869(459-468)Online publication date: 19-Jul-2010
https://dl.acm.org/doi/10.5555/1886811.1886869
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Cluster Graph Modification Problems
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
    2. Graph theory

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Published In

cover image Guide Proceedings

WG '02: Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science

June 2002

420 pages

ISBN:3540003312

Editor:
Ludek Kucera

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 13 June 2002

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Cited By

Bulhes Tde Sousa Filho GSubramanian ACabral L(2017)Branch-and-cut approaches for p-Cluster EditingDiscrete Applied Mathematics10.1016/j.dam.2016.10.026219:C(51-64)Online publication date: 11-Mar-2017
https://dl.acm.org/doi/10.1016/j.dam.2016.10.026
Bulhões TSubramanian ASousa Filho GCabral L(2017)Branch-and-price for p-cluster editingComputational Optimization and Applications10.1007/s10589-017-9893-x67:2(293-316)Online publication date: 1-Jun-2017
https://dl.acm.org/doi/10.1007/s10589-017-9893-x
Chen JMeng J(2010)A 2k Kernel for the cluster editing problemProceedings of the 16th annual international conference on Computing and combinatorics10.5555/1886811.1886869(459-468)Online publication date: 19-Jul-2010
https://dl.acm.org/doi/10.5555/1886811.1886869
Zhang RLiu JHan ZZheng L(2010)An IBE scheme using ECC combined public keyComputers and Electrical Engineering10.1016/j.compeleceng.2010.03.00636:6(1046-1054)Online publication date: 1-Nov-2010
https://dl.acm.org/doi/10.1016/j.compeleceng.2010.03.006
Brandes UGaertler MWagner D(2008)Engineering graph clusteringACM Journal of Experimental Algorithmics10.1145/1227161.122716212(1-26)Online publication date: 12-Jun-2008
https://dl.acm.org/doi/10.1145/1227161.1227162
Tan J(2008)A note on the inapproximability of correlation clusteringInformation Processing Letters10.1016/j.ipl.2008.06.004108:5(331-335)Online publication date: 1-Nov-2008
https://dl.acm.org/doi/10.1016/j.ipl.2008.06.004
Chaudhuri KHalperin ERao SZhou SGabow H(2007)A rigorous analysis of population stratification with limited dataProceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms10.5555/1283383.1283496(1046-1055)Online publication date: 7-Jan-2007
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Schaeffer S(2007)SurveyComputer Science Review10.1016/j.cosrev.2007.05.0011:1(27-64)Online publication date: 1-Aug-2007
https://dl.acm.org/doi/10.1016/j.cosrev.2007.05.001
Dessmark AJansson JLingas ALundell EPersson M(2006)On the approximability of maximum and minimum edge clique partition problemsProceedings of the Twelfth Computing: The Australasian Theory Symposium - Volume 5110.5555/2523791.2523805(101-105)Online publication date: 16-Jan-2006
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Dessmark AJansson JLingas ALundell EPersson M(2006)On the approximability of maximum and minimum edge clique partition problemsProceedings of the 12th Computing: The Australasian Theroy Symposium - Volume 5110.5555/1151785.1151797(101-105)Online publication date: 1-Jan-2006
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