Vertex and edge covers with clustering properties: complexity and algorithms

Fernau, H. and Manlove, D.F. (2009) Vertex and edge covers with clustering properties: complexity and algorithms. Journal of Discrete Algorithms, 7(2), pp. 149-167. (doi:10.1016/j.jda.2008.09.007)

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Abstract

We consider the concepts of a t-total vertex cover and a t-total edge cover (t≥1), which generalise the notions of a vertex cover and an edge cover, respectively. A t-total vertex (respectively edge) cover of a connected graph G is a vertex (edge) cover S of G such that each connected component of the subgraph of G induced by S has at least t vertices (edges). These definitions are motivated by combining the concepts of clustering and covering in graphs. Moreover they yield a spectrum of parameters that essentially range from a vertex cover to a connected vertex cover (in the vertex case) and from an edge cover to a spanning tree (in the edge case). For various values of t, we present NP-completeness and approximability results (both upper and lower bounds) and FTP algorithms for problems concerned with finding the minimum size of a t-total vertex cover, t-total edge cover and connected vertex cover, in particular improving on a previous FTP algorithm for the latter problem.

Item Type:Articles
Keywords:T-total vertex cover, connected vertex cover, t-total edge cover, polynomial-time algorithm, NP-completeness, approximation algorithm, FPT algorithm
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Professor David
Authors: Fernau, H., and Manlove, D.F.
Subjects:Q Science > QA Mathematics > QA75 Electronic computers. Computer science
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Journal of Discrete Algorithms
Publisher:Elsevier
ISSN:1570-8667
ISSN (Online):1570-8675
Published Online:23 September 2008
Copyright Holders:Copyright © 2009 Elsevier
First Published:First published in Journal of Discrete Algorithms 7(2):149-167
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
409961The Glasgow computing science research festival 2005Muffy CalderEngineering & Physical Sciences Research Council (EPSRC)EP/D030110/1Computing Science
436361MATCH-UP - matching under preferences - algorithms and complexityRobert IrvingEngineering & Physical Sciences Research Council (EPSRC)EP/E011993/1COM - COMPUTING SCIENCE