Randomized algorithms and upper bounds for multiple domination in graphs and networks

Authors:
Andrei Gagarin;Anush Poghosyan;Vadim Zverovich
Affiliations:
Department of Mathematics and Statistics, Acadia University, Wolfville, Nova Scotia, B4P 2R6, Canada;Department of Mathematics and Statistics, University of the West of England, Bristol, BS16 1QY, UK;Department of Mathematics and Statistics, University of the West of England, Bristol, BS16 1QY, UK
Venue:
Discrete Applied Mathematics
Year:
2013

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Abstract

We consider four different types of multiple domination and provide new improved upper bounds for the k- and k-tuple domination numbers. They generalize two classical bounds for the domination number and are better than a number of known upper bounds for these two multiple domination parameters. Also, we explicitly present and systematize randomized algorithms for finding multiple dominating sets, whose expected orders satisfy new and recent upper bounds. The algorithms for k- and k-tuple dominating sets are of linear time in terms of the number of edges of the input graph, and they can be implemented as local distributed algorithms. Note that the corresponding multiple domination problems are known to be NP-complete.