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Tight bounds for parameterized complexity of cluster editing with a small number of clusters

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Fomin, Fedor V., Kratsch, Stefan, Pilipczuk, Marcin, Pilipczuk, Michał and Villanger, Yngve (2014) Tight bounds for parameterized complexity of cluster editing with a small number of clusters. Journal of Computer and System Sciences, Volume 80 (Number 7). pp. 1430-1447. doi:10.1016/j.jcss.2014.04.015 ISSN 0022-0000.

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Official URL: http://dx.doi.org/10.1016/j.jcss.2014.04.015

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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 View the MathML source 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(kσ) such that there is no algorithm deciding in time View the MathML source whether G can be transformed into a cluster graph with at most p cliques by changing at most k adjacencies.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH): Cluster analysis, Graph theory
Journal or Publication Title: Journal of Computer and System Sciences
Publisher: Academic Press
ISSN: 0022-0000
Official Date: November 2014
Dates:
DateEvent
November 2014Published
16 April 2014Available
8 April 2014Accepted
3 May 2013Submitted
Volume: Volume 80
Number: Number 7
Page Range: pp. 1430-1447
DOI: 10.1016/j.jcss.2014.04.015
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: Seventh Framework Programme (European Commission) (FP7), European Research Council (ERC), Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Netherlands Organisation for Scientific Research] (NWO), Narodowe Centrum Nauki (NCN), Fundacja na rzecz Nauki Polskiej [Foundation for Polish Science] (FNP)
Grant number: 267959 (ERC), N206 567140 (NCN)
Embodied As: 1

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