Subexponential fixed-parameter tractability of cluster editing

Details Subexponential fixed-parameter tractability of cluster editing Subexponential fixed-parameter tractability of cluster editing

2011-12-19

arxiv.org/abs/1112.4419v3

Computer Science

Computational Complexity

New version contains significantly new results: deterministic algorithm and a multivariate lower bound

Scientific paper

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 complement 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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