A self-stabilizing protocol for minimal weighted dominating sets in arbitrary networks

A lot of self-stabilizing algorithms for computing dominating sets problem have been proposed in the literature due to many real-life applications. Most of the proposed algorithms either work for dominating sets with a uniform weight or find approximation solutions to weighted dominating sets. However, for non-uniform weighted dominating sets (WDS) problem, there is no self-stabilizing algorithm for the WDS. Furthermore, how to find the minimal weighted dominating set is a challenge. In this paper, we propose a self-stabilizing algorithm for the minimal weighted dominating set (MWDS) 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