General approximation schemes for min-max (regret) versions of some (pseudo-)polynomial problems

While the complexity of min-max and min-max regret versions of most classical combinatorial optimization problems has been thoroughly investigated, there are very few studies about their approximation. For a bounded number of scenarios, we establish general approximation schemes which can be used for min-max and min-max regret versions of some polynomial or pseudo-polynomial problems. Applying these schemes to shortest path, minimum spanning tree, minimum weighted perfect matching on planar graphs, and knapsack problems, we obtain fully polynomial-time approximation schemes with better running times than the ones previously presented in the literature.