On the Complexity of Min-Max Optimization Problems and their Approximation

The computational complexity of optimization problems of the min-max form is naturally characterized by ∏ 2 P , the second level of the polynomial-time hierarchy. We present a number of optimization problems of this form and show that they are complete for the class ∏ 2 P . We also show that the constant–factor approximation versions of some of these optimization problems are also complete for ∏ 2 P .