UNIVERSITY of GLASGOW

Computing at Glasgow University
 
Paper ID: 8137
DCS Tech Report Number: TR-2006-210

Vertex and Edge Covers with Clustering Properties: Complexity and Algorithms
Fernau,H. Manlove,D.F.

Publication Type: Tech Report (internal)
Appeared in: DCS Technical Report Series
Page Numbers :
Publisher: Dept of Computing Science, University of Glasgow
Year: 2006
Abstract:

We consider the concepts of a t-total vertex cover and a t-total edge cover (t>=1), which generalize 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 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 FPT 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 FPT algorithm for the latter problem.

Keywords: Algorithm; NP-completeness; approximability; t-total vertex cover; connected vertex cover; t-total edge cover


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