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

Gagarin, Andrei; Poghosyan, Anush; Zverovich, Vadim

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. © 2011 Elsevier B.V. All rights reserved.

• Presentation Conference Type: Conference Paper (published)
• Publication Date: Mar 1, 2013
• Deposit Date: Oct 27, 2011
• Publicly Available Date: Feb 26, 2016
• Journal: Discrete Applied Mathematics
• Print ISSN: 0166-218X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 161
• Issue: 4-5
• Pages: 604-611
• DOI: https://doi.org/10.1016/j.dam.2011.07.004
• Keywords: randomized algorithm, k-domination, k-tuple domination, α-domination, α-rate domination
• Public URL: https://uwe-repository.worktribe.com/output/934293
• Publisher URL: http://dx.doi.org/10.1016/j.dam.2011.07.004
• Contract Date: Feb 26, 2016