Distributed distance domination in graphs with no K_2,t-minor

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 ϵ>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+ϵ) of the optimum. The algorithm runs in O(log^⁎⁡|V|) rounds in the Local model. In particular, both algorithms work in outerplanar graphs.