Dominating sets in directed graphs

Authors:
Chaoyi Pang;Rui Zhang;Qing Zhang;Junhu Wang
Affiliations:
The Australian e-Health Research Centre, ICT Centre, CSIRO, Australia;Department of Computer Science and Software Engineering, The University of Melbourne, Australia;The Australian e-Health Research Centre, ICT Centre, CSIRO, Australia;School of Information and Communication Technology, Griffith University, Australia
Venue:
Information Sciences: an International Journal
Year:
2010

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Abstract

We consider the problem of incrementally computing a minimal dominating set of a directed graph after the insertion or deletion of a set of arcs. Earlier results have either focused on the study of the properties that minimum (not minimal) dominating sets preserved or lacked to investigate which update affects a minimal dominating set and in what ways. In this paper, we first show how to incrementally compute a minimal dominating set on arc insertions. We then reduce the case of computing a minimal dominating set on arc deletions to the case of insertions. Some properties on minimal dominating sets are provided to support the incremental strategy. Lastly, we give a new bound on the size of minimum dominating sets based on those results.