A self-stabilizing algorithm for finding a minimal 2-dominating set assuming the distributed demon model

Abstract

A 2-dominating set in a distributed system is a set of processors such that each processor outside the set has at least two neighbors in the set. In applications, a 2-dominating set can be considered as an ideal place in the system for allocating resources, and a minimal 2-dominating set allows for the minimum of resources to be allocated. Since a maximal independent set can be viewed as a minimal 1-dominating set, the problem of finding a minimal 2-dominating set extends the problem of finding a maximal independent set in some sense. The distributed demon model for self-stabilizing systems is a natural generalization of the central demon model introduced by Dijkstra. In the past, only a few self-stabilizing algorithms under the distributed demon model have been obtained without using any transformer, and most of these algorithms are for ring networks only. In this paper, we propose a self-stabilizing algorithm that can find a minimal 2-dominating set in any general network in which the distributed demon model is assumed. This proposed algorithm is not obtained via any transformer. We also verify the correctness of the proposed algorithm.