Distributed distance domination in graphs with no $K_{2,t}$-minor

Abstract

We prove that a simple distributed algorithm finds a constant approximation of an optimal distance-k dominating set in graphs with no K 2,t -minor. The algorithm runs in a constant number of rounds. We further show how this procedure can be used to give a distributed algorithm which given > 0 and k, t ∈ Z + finds in a graph G = (V, E) with no K 2,t -minor a distance-k dominating set of size at most (1 + ) of the optimum. The algorithm runs in O(log * |V |) rounds in the Local model. In particular, both algorithms work in outerplanar graphs.