Abstract
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.
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Damaschke, P. (2006). Fixed-Parameter Tractable Generalizations of Cluster Editing. In: Calamoneri, T., Finocchi, I., Italiano, G.F. (eds) Algorithms and Complexity. CIAC 2006. Lecture Notes in Computer Science, vol 3998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758471_33
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DOI: https://doi.org/10.1007/11758471_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34375-2
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