A Self-stabilizing Algorithm for Finding a Minimal K-Dominating Set in General Networks
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Since the publication of Dijkstra’s pioneering paper, a lot of self-stabilizing algorithms for computing dominating sets have been proposed in the literature. However, there is no self-stabilizing algorithm for the minimal k-dominating set (MKDS) in arbitrary graphs that works under a distributed daemon. The proposed algorithms for the minimal k-dominating set (MKDS) either work for trees (Kamei and Kakugawa ) or find a minimal 2-dominating set (Huang et al. [14,15]). In this paper, we propose a self-stabilizing algorithm for the minimal k-dominating set (MKDS) under a central daemon model when operating in any general network. We further prove that the worst case convergence time of the algorithm from any arbitrary initial state is O(n 2) steps where n is the number of nodes in the network.
KeywordsSelf-stabilizing algorithm Minimal k-dominating set Central daemon model General network Convergence
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