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- W1985427743 abstract "In the Cluster Editing problem, also known as Correlation Clustering , 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-time parameterized algorithm that in time 2 O ( p k ) + n O ( 1 ) decides whether G can be transformed into a cluster graph with exactly p cliques by changing at most k adjacencies. Our algorithmic findings are complemented by the following tight lower bound on the asymptotic behavior of our algorithm. We show that unless ETH fails, for any constant 0 < σ ≤ 1 , there is p = Θ ( k σ ) such that there is no algorithm deciding in time 2 o ( p k ) ⋅ n O ( 1 ) whether G can be transformed into a cluster graph with at most p cliques by changing at most k adjacencies. • The problem is to partition a graph into cliques by editing a small number of edges. • We study the problem from the perspective of parameterized complexity. • We give a parameterized algorithm. • The running time is subexponential if the target number of clusters is sublinear. • We show that the running time of our algorithm is tight assuming ETH." @default.
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- W1985427743 date "2014-11-01" @default.
- W1985427743 modified "2023-10-17" @default.
- W1985427743 title "Tight bounds for parameterized complexity of Cluster Editing with a small number of clusters" @default.
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- W1985427743 doi "https://doi.org/10.1016/j.jcss.2014.04.015" @default.
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