Memory Efficient Self-Stabilizing k-Independent Dominating Set Construction

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. keywords distributed computing, fault tolerance, self-stabilization, k-dominating set, k-independent set, k-independent dominating set, memory efficient