### Subexponential fixed-parameter tractability of cluster editing [article]

Fedor V. Fomin and Stefan Kratsch and Marcin Pilipczuk and Michał Pilipczuk and Yngve Villanger
<span title="2013-01-30">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In the Correlation Clustering, also known as Cluster Editing, we are given an undirected n-vertex graph G and a positive integer k. The task is to decide if G can be transformed into a cluster graph, i.e., a disjoint union of cliques, by changing at most k adjacencies, i.e. by adding/deleting at most k edges. We give a subexponential algorithm that, in time 2^O(sqrt(pk)) + n^O(1) decides whether G can be transformed into a cluster graph with p cliques by changing at most k adjacencies. We
more &raquo; ... ment our algorithmic findings by the following tight lower bounds on the asymptotic behaviour of our algorithm. We show that, unless ETH fails, for any constant 0 < s <= 1, there is p = Theta(k^s) such that there is no algorithm deciding in time 2^o(sqrt(pk)) n^O(1) whether G can be transformed into a cluster graph with p cliques by changing at most k adjacencies.
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