Cyclic games and an algorithm to find minimax cycle means in directed graphs
USSR Computational Mathematics and Mathematical Physics
A subexponential randomized simplex algorithm (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
The complexity of stochastic games
Information and Computation
The P-matrix problem is co-NP-complete
Mathematical Programming: Series A and B
Linear programming, the simplex algorithm and simple polytopes
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
The Generalized Linear Complementarity Problem: Least Element Theory andZ-Matrices
Journal of Global Optimization
Combinatorial structure and randomized subexponential algorithms for infinite games
Theoretical Computer Science
A combinatorial strongly subexponential strategy improvement algorithm for mean payoff games
Discrete Applied Mathematics
Cyclic games and linear programming
Discrete Applied Mathematics
A Simple P-Matrix Linear Complementarity Problem for Discounted Games
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Algorithms for Solving Infinite Games
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Linear Complementarity Algorithms for Infinite Games
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
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We define the first nontrivial polynomially recognizable subclass of P-matrixGeneralized Linear Complementarity Problems (GLCPs) with a subexponential pivot rule. No such classes/rules were previously known. We show that a subclass of Shapley turn-based stochastic games, subsuming Condon's simple stochastic games, is reducible to the new class of GLCPs. Based on this we suggest the new strongly subexponential combinatorial algorithms for these games.