In this paper, we introduce a domination-related problem called Harmless Set: given a graph G = (V,E), a threshold function t : V → N and an integer k, find a subset of vertices V ′ ⊆ V of size at least k such that every vertex v in V has less than t(v) neighbors in V ′. We study its parameterized complexity and the approximation of the associated… (More)