Memory efficient Self - Stabilizing k - Independant Dominating Set Construction ?

We propose a memory efficient self-stabilizing protocol building k-independant dominating sets. A k-independant dominating set is a k-independant set and a k-dominating set. A set of nodes, I, is kindependent 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). The built kindependant dominating sets contain at most b2n/k + 2c nodes, n being the network size. The protocol SID is memory efficient : it requires only 2log((k+1)n+1) bits per node. The correctness and the terminaison of the protocol SID is proven. keywords distributed computing, fault tolerance, self-stabilization, kdominating set, k-independant set, k-independant dominating set