Memory Efficient Self-Stabilizing k-Independent Dominating Set Construction

Abstract

We propose a memory efficient self-stabilizing protocol building k-independent dominating sets. A k-independent dominating set is a k-independent set and a kdominating set. A set of nodes, I, is k-independent if the distance between any pair of nodes in I is at least k + 1. A set of nodes, D, is a k-dominating if every node is within distance k of a node of D. Our algorithm, named SID, is silent; it converges under the unfair distributed scheduler (the weakest scheduling assumption). We established that any k-independent sets contains at most (2n)/(k + 2) nodes, n being the network size. The protocol SID is memory efficient : it requires only 2log((k + 1)n + 1) + 1 bits per node. The correctness and the termination of the protocol SID is proven. The computation of the convergence time of the protocol SID is opened question.