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<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6ovb2qpkfenhmb7mcksobrcxq" style="color: black;">Journal of computer and system sciences (Print)</a>
A note on versions: The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP url' above for details on accessing the published version and note that access may require a subscription. For more information, please contact the WRAP Team at: firstname.lastname@example.org Tight bounds for parameterized complexity of Cluster Editing with a small number of<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcss.2014.04.015">doi:10.1016/j.jcss.2014.04.015</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hc7pkihgofdrxj5gz7fvgxsptu">fatcat:hc7pkihgofdrxj5gz7fvgxsptu</a> </span>
more »... rs $ 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( √ pk) + 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( √ pk) · n O(1) whether G can be transformed into a cluster graph with at most p cliques by changing at most k adjacencies.
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