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2010

Fixed-Parameter Enumerability of Cluster Editing and Related Problems

13 years 7 months ago
Fixed-Parameter Enumerability of Cluster Editing and Related Problems
Cluster Editing is transforming a graph by at most k edge insertions or deletions into a disjoint union of cliques. This problem is fixed-parameter tractable (FPT). Here we compute concise enumerations of all minimal solutions in O(2.27k + k2n + m) time. Such enumerations support efficient inference procedures, but also the optimization of further objectives such as minimizing the number of clusters. In an extended problem version, target graphs may have a limited number of overlaps of cliques, measured by the number t of edges that remain when the twin vertices are merged. This problem is still in FPT, with respect to the combined parameter k and t. The result is based on a property of twin-free graphs. We also give FPT results for problem versions avoiding certain artificial clusterings. Furthermore, we prove that all solutions with minimal edit sequences differ on a so-called full kernel with at most k2/4 + O(k) vertices, that can be found in polynomial time. The size bound is tigh...
Peter Damaschke
Added 20 May 2011
Updated 20 May 2011
Type Journal
Year 2010
Where MST
Authors Peter Damaschke
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