Solving Min-Max Problems with Applications to Games

TL;DR

This paper advances network optimization methods to efficiently solve a range of min-max problems, including new variants of game and interdiction problems, with nearly linear algorithms and novel problem characterizations.

Contribution

It introduces refined techniques for network optimization, new problem characterizations, and applies these to solve complex two-player games efficiently.

Findings

Nearly linear time algorithms for certain two-player games

New variant of network interdiction problem with vertex-wise budget

Applicable to mean payoff games with maximum weight instead of limit average

Abstract

We refine existing general network optimization techniques, give new characterizations for the class of problems to which they can be applied, and show that they can also be used to solve various two-player games in almost linear time. Among these is a new variant of the network interdiction problem, where the interdictor wants to destroy high-capacity paths from the source to the destination using a vertex-wise limited budget of arc removals. We also show that replacing the limit average in mean payoff games by the maximum weight results in a class of games amenable to these techniques.