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)

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.

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
40996	1	The Glasgow computing science research festival 2005	Muffy Calder	Engineering & Physical Sciences Research Council (EPSRC)	EP/D030110/1	Computing Science
43636	1	MATCH-UP - matching under preferences - algorithms and complexity	Robert Irving	Engineering & Physical Sciences Research Council (EPSRC)	EP/E011993/1	COM - COMPUTING SCIENCE