Approximations for Restrictions of The Budgeted and Generalized Maximum Coverage Problems

In this paper we present approximation preserving reductions from the Budgeted and Generalized Maximum Coverage Problems to the Knapsack Problem with Conflict Graphs. The reductions are used to yield Polynomial Time Approximation Schemes for special classes of instances of these problems. Using these approximation schemes, the existence of pseudo-polynomial algorithms are proven and, in more particular cases, these algorithms are shown to have polynomial time complexity. Moreover, the characteristics of the instances that admit these algorithms are analyzed.