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 - 2002/1/1
Y1 - 2002/1/1
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
M3 - Conference contribution
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 -