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

Gagarin, Andrei; Poghosyan, Anush; Zverovich, Vadim

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


Authors

Andrei Gagarin

Anush Poghosyan



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.

Citation

Gagarin, A., Poghosyan, A., & Zverovich, V. (2013). Randomized algorithms and upper bounds for multiple domination in graphs and networks. Discrete Applied Mathematics, 161(4-5), 604-611. https://doi.org/10.1016/j.dam.2011.07.004

Journal Article Type Conference Paper
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

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