Fixed-Parameter Tractable Generalizations of Cluster Editing

  • Peter Damaschke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3998)


In the Cluster Editing problem, a graph has to be changed to a disjoint union of cliques by at most k edge insertions or deletions. Several reasons suggest a generalized problem where the target graph can have some overlapping cliques. We show that the problem remains fixed-parameter tractable (FPT) in the combination of both parameters: k and a second parameter t describing somehow the complexity of overlap structure. For this result we need a structural property of twins in graphs enabling a certain elimination scheme that finally leads to a small enough subgraph we can branch on. We also give a nontrivial algorithm for problem minimizing the number of disjoint clusters, based on a concise enumeration of all solutions to the original Cluster Editing problem. This generic scheme may become interesting also for other multicriteria FPT problems.


Search Tree Vertex Cover Minimal Solution Cluster Graph Natural Cluster 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Peter Damaschke
    • 1
  1. 1.School of Computer Science and EngineeringChalmers UniversityGöteborgSweden

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