Fixed-parameter enumerability of cluster editing and related problems
Artikel i vetenskaplig tidskrift, 2010

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(2.27^k+k^2n+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 k^2/4+O(k) vertices, that can be found in polynomial time. The size bound is tight. We also get a bound for the number of edges in the full kernel, which is optimal up to a (large) constant factor. Numerous open problems are mentioned.

enumeration problems

fixed-parameter tractability

soft clustering

true twins

cluster graphs

Författare

Peter Damaschke

Chalmers, Data- och informationsteknik, Datavetenskap

Theory of Computing Systems

1432-4350 (ISSN) 1433-0490 (eISSN)

Vol. 46 261-283

Ämneskategorier

Datavetenskap (datalogi)

DOI

10.1007/s00224-008-9130-1