Efficient self-stabilizing algorithms for minimal total k-dominating sets in graphs

Authors:
Yacine Belhoul;Saïd Yahiaoui;Hamamache Kheddouci
Affiliations:
Département d'Informatique, Université A/Mira, 06000, Bejaia, Algeria and CERIST, Ben Aknoun, 16030, Algiers, Algeria;Département d'Informatique, Université A/Mira, 06000, Bejaia, Algeria and CERIST, Ben Aknoun, 16030, Algiers, Algeria;Université de Lyon, CNRS, Université Lyon 1, LIRIS, UMR5205 F-69622, France
Venue:
Information Processing Letters
Year:
2014

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Abstract

We propose the first polynomial self-stabilizing distributed algorithm for the minimal total dominating set problem in an arbitrary graph. Then, we generalize the proposed algorithm for the minimal total k-dominating set problem. Under an unfair distributed scheduler, the proposed algorithms converge in O(mn) moves starting from any arbitrary state, and require O(logn) storage per node.