Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Cluster analysis and mathematical programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Clustering Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
IEEE Transactions on Pattern Analysis and Machine Intelligence
Center CLICK: A Clustering Algorithm with Applications to Gene Expression Analysis
Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology
Graphs and Hypergraphs
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
Cluster graph modification problems
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
Correlation clustering with a fixed number of clusters
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Clustering with qualitative information
Journal of Computer and System Sciences - Special issue: Learning theory 2003
On the approximability of maximum and minimum edge clique partition problems
CATS '06 Proceedings of the 12th Computing: The Australasian Theroy Symposium - Volume 51
Engineering graph clustering: Models and experimental evaluation
Journal of Experimental Algorithmics (JEA)
A threshold criterion, auto-detection and its use in MST-based clustering
Intelligent Data Analysis
A rigorous analysis of population stratification with limited data
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A note on the inapproximability of correlation clustering
Information Processing Letters
Cluster graph modification problems
Discrete Applied Mathematics
Graph-modeled data clustering: fixed-parameter algorithms for clique generation
CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
A 2k Kernel for the cluster editing problem
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
On the NP-Completeness of some graph cluster measures
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
Fixed-parameter tractable generalizations of cluster editing
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
On the fixed-parameter enumerability of cluster editing
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Error compensation in leaf root problems
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Computer Science Review
Efficient parameterized preprocessing for cluster editing
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
On the approximability of maximum and minimum edge clique partition problems
CATS '06 Proceedings of the Twelfth Computing: The Australasian Theory Symposium - Volume 51
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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 驴 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.