Considering the collection of all networks with independent set interference model, Shah, Tse, and Tsitsiklis showed that there exist scheduling algorithms with polynomial complexity and delay, only if the maximum independent set problem can be solved in polynomial time (equivalently, P=NP). In this paper, we extend this result to arbitrary collections of networks and present a clear-cut criterion for the existence of polynomial complexity and delay scheduling algorithms relative to a given collection of networks with arbitrary interference models, not confined to independent set interference or SINR models, and not necessarily encompassing all network topologies. This amounts to the equivalence of polynomial scheduling and effective approximation of maximum weighted actions.