Minimising K-Dominating Set in Arbitrary Network Graphs

Abstract

A self-stabilizing algorithm, after transient faults hit the system and place it in some arbitrary global state, recovers in finite time without external e.g., human intervention. A k-dominating set in a distributed system is a set of processors such that each processor outside the set has at least k neighbors in the set. In the past, a few self-stabilizing algorithms for minimal k-dominating set MKDS have been obtained. However, the presented self-stabilizing algorithms for MKDS work for either trees or a minimal 2-dominating set. Recently a self-stabilizing algorithm for MKDS in arbitrary graphs under a central daemon has been investigated. But so far, there is no algorithm for the MKDS problem in arbitrary graphs that works under a distributed daemon. In this paper, we propose a self-stabilizing algorithm for finding a MKDS under a distributed daemon model when operating in any general network graph. We further verify the correctness of the proposed algorithm Algorithm MKDS and prove that the worst case convergence time of the algorithm from any arbitrary initial state is On 2 steps where n is the number of nodes in the network.