We consider approximating the minmax value of a multiplayer game in strategic form. Tightening recent bounds by Borgs et al., we observe that approximating the value with a precision of ǫ log n digits (for any constant ǫ > 0) is NP-hard, where n is the size of the game. On the other hand, approximating the value with a precision of c log log n digits (for any constant c ≥ 1) can be done in quas...

In a recent paper [10], an algorithmic approach was presented for the robust (minmax regret) absolute deviation location problem on networks with vertex weights which are linear functions of an uncertain or dynamically changing parameter. In this paper, we present algorithmic and analytical improvements that significantly reduce the computational complexity bounds for the algorithm.

In this paper, we provide a generic anytime lower bounding procedure for minmax regret optimization problems. We show that the lower bound obtained is always at least as accurate as the lower bound recently proposed by Chassein and Goerigk [2]. The validity of the bound is based on game theoretic arguments and its computation is performed via a double oracle algorithm [6] that we specify. The l...

The design of control laws for systems subject to complex state constraints still presents a significant challenge. This paper explores a dynamic programming approach to a specific class of such problems, that of reachability under state constraints. The problems are formulated in terms of nonstandard minmax and maxmin cost functionals, and the corresponding value functions are given in terms o...

In this paper we discuss a minmax regret version of the single machine scheduling problem with the total flow time criterion. Uncertain processing times are modeled by closed intervals. We show that if the deterministic problem is polynomially solvable, then its minmax regret version is approximable within 2.

The minmax regret problem for combinatorial optimization under uncertainty can be viewed as a zero-sum game played between an optimizing player and an adversary, where the optimizing player selects a solution and the adversary selects costs with the intention of maximizing the regret of the player. Existing minmax regret models consider only deterministic solutions/strategies, and minmax regret...

We consider the minmax regret 1-center problem on a general network with uncertainty on demands. Unlike other papers which considered the problem under interval uncertainty, we assume here that demand uncertainty is modelled by a finite number of discrete scenarios. We develop a solution approach based on the decomposition of the network into basic intervals and present a polynomial algorithm f...

This paper addresses a version of the single-facility Maximal Covering Location Problem on network where demand is: (i) distributed along edges and (ii) uncertain with only known interval estimation. To deal this problem, we propose minmax regret model service facility can be located anywhere network. problem is called Minmax Regret (MMR-EMCLP). Furthermore, present two polynomial algorithms fo...