Self-Stabilizing Maximal K-Dependent Sets In Linear Time

In a graph or network G = (V;E), a set S V is k-dependent if no node in S has more than k neighbors in S. We show that for each k 0 there is a self-stabilizing algorithm that identi es a maximal k-dependent set, and stabilizes in O(m + n) time. An interesting by-product of our paper is the new result that in any graph there exists a set that is both maximal k-dependent and minimal (k+1)-dominating. The set selected by our algorithm, in fact, has this property.