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

Sayaka KAMEI  Hirotsugu KAKUGAWA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E88-A   No.5   pp.1109-1116
Publication Date: 2005/05/01
Online ISSN: 
DOI: 10.1093/ietfec/e88-a.5.1109
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: 
Keyword: 
self-stabilizing distributed algorithm,  fault-tolerance,  approximation,  minimum k-dominating set,  general networks,  

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Summary: 
Self-stabilization is a theoretical framework of non-masking 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 , where Δ is the maximum degree of G, in the networks of which the minimum degree is more than or equal to k.