In this paper, we consider the TARGET SET SELECTION problem: given a graph and a threshold value thr(v) for each vertex v of the graph, find a minimum size vertex-subset to “activate” such that all vertices of the graph are activated at the end of th

Given a family of subsets 𝒮 over a set of elements X and two integers p and k, max k-set cover consists of finding a subfamily 𝒯 ⊆ 𝒮 of cardinality at most k, covering at least p elements of X. This problem is W[2]-hard when parameterized by k, and FPT when parameterized by p. We investigate the parameterized approximability of the problem with respect to parameters k and p. Then, we show that max sat-k, a satisfiability problem generalizing max k-set cover, is also FPT with respect to parameter p.