Approximating min-max (regret) versions of some polynomial problems

Abstract

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 a general approximation scheme which can be used for min-max and min-max regret versions of some polynomial problems. Applying this scheme to shortest path and minimum spanning tree, we obtain fully polynomial-time approximation schemes with much better running times than the ones previously presented in the literature. © Springer-Verlag Berlin Heidelberg 2006.