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

Gagarin, A., Poghosyan, A. and Zverovich, V. (2013) Randomized algorithms and upper bounds for multiple domination in graphs and networks. Discrete Applied Mathematics, 161 (4-5). pp. 604-611. ISSN 0166-218X

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Publisher's URL: http://dx.doi.org/10.1016/j.dam.2011.07.004

Abstract

We consider four different types of multiple domination and provide new improved upper bounds for the k- and k-tuple domination numbers. They generalise 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.

Item Type:Article
Uncontrolled Keywords:randomized algorithm, k-domination, k-tuple domination, α-domination, α-rate domination
Faculty/Department:Faculty of Environment and Technology
ID Code:15867
Deposited By: Dr V. Zverovich
Deposited On:27 Oct 2011 15:46
Last Modified:18 Aug 2013 21:55

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