Fast Fixed-Parameter Tractable Algorithms for Nontrivial Generalizations of Vertex Cover
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Phylogenetic k-Root and Steiner k-Root
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Cluster Graph Modification Problems
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Machine Learning
Parameterized enumeration, transversals, and imperfect phylogeny reconstruction
Theoretical Computer Science - Parameterized and exact computation
Graph-modeled data clustering: fixed-parameter algorithms for clique generation
CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
Gene network: model, dynamics and simulation
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
On the fixed-parameter enumerability of cluster editing
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity
The cluster editing problem: implementations and experiments
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Efficient parameterized preprocessing for cluster editing
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
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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.