A Self-Stabilizing Approximation Algorithm for the Distributed Minimum k-Domination*

Authors:
Sayaka Kamei;Hirotsugu Kakugawa
Affiliations:
The authors are with the Department of Information Engineering, Hiroshima University, Higashihiroshima-shi, 739-8527 Japan. E-mail: saya@aial.hiroshima-u.ac.jp E-mail: h.kakugawa@computer.org;The authors are with the Department of Information Engineering, Hiroshima University, Higashihiroshima-shi, 739-8527 Japan. E-mail: saya@aial.hiroshima-u.ac.jp E-mail: h.kakugawa@computer.org
Venue:
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Year:
2005

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Abstract

Self-stabilization is a theoretical framework of nonmasking fault-tolerant distributed algorithms. In this paper, we investigate a self-stabilizing distributed approximation for the minimum k-dominating set (KDS) problem in general networks. The minimum KDS problem is a generalization of the well-known dominating set problem in graph theory. For a graph G = (V, E), a set Dk ⊆ V is a KDS of G if and only if each vertex not in Dk is adjacent to at least k vertices in Dk. The approximation ratio of our algorithm is Δ/k(1 + (k-1/Δ+1)), where Δ is the maximum degree of G, in the networks of which the minimum degree is more than or equal to k.