Even faster parameterized cluster deletion and cluster editing
Journal article, 2011
Cluster Deletion and Cluster Editing ask to transform a graph
by at most k edge deletions or edge edits, respectively, into a cluster
graph, i.e., disjoint union of cliques. Equivalently, a cluster graph has
no conflict triples, i.e., two incident edges without a transitive edge.
We solve the two problems in time O(1.415^k) and O(1.76^k), respectively. These results round off our earlier work by considerably
improved time bounds. For Cluster Deletion we use a technique that
cuts away small connected components that do no longer contribute to the
exponential part of the time complexity. As this idea is simple and
versatile, it may lead to improvements for several other parameterized
graph problems. The improvement for Cluster Editing is achieved by
using the full power of an earlier structure theorem for graphs where no
edge is in three conflict triples.