TY - GEN

T1 - Cluster graph modification problems

AU - Shamir, Ron

AU - Sharan, Roded

AU - Tsur, Dekel

N1 - Funding Information:
R. Shamir was supported in part by the Israel Science Foundation (grants number 565/99 and 309/02). R. Sharan was supported by a Fulbright grant and by an Eshkol fellowship from the Ministry of Science, Israel.

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84901476329&partnerID=8YFLogxK

U2 - 10.1007/3-540-36379-3_33

DO - 10.1007/3-540-36379-3_33

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AN - SCOPUS:84901476329

SN - 3540003312

SN - 9783540003311

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 379

EP - 390

BT - Graph-Theoretic Concepts in Computer Science - 28th International Workshop, WG 2002, Revised Papers

A2 - Kucera, Ludek

PB - Springer Verlag

T2 - 28th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2002

Y2 - 13 June 2002 through 15 June 2002

ER -