Cyclic games and an algorithm to find minimax cycle means in directed graphs
USSR Computational Mathematics and Mathematical Physics
The complexity of stochastic games
Information and Computation
The complexity of mean payoff games on graphs
Theoretical Computer Science
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
A Discrete Strategy Improvement Algorithm for Solving Parity Games
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
A Cycle Time Computing Algorithm and its Application in the Structural Analysis of Min-max Systems
Discrete Event Dynamic Systems
A deterministic subexponential algorithm for solving parity games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A policy iteration algorithm for computing fixed points in static analysis of programs
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Max-plus Algebraic Tools for Discrete Event Systems, Static Analysis, and Zero-Sum Games
FORMATS '09 Proceedings of the 7th International Conference on Formal Modeling and Analysis of Timed Systems
Faster algorithms for mean-payoff games
Formal Methods in System Design
Brief paper: On the control of max-plus linear system subject to state restriction
Automatica (Journal of IFAC)
A pumping algorithm for ergodic stochastic mean payoff games with perfect information
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Tropical linear-fractional programming and parametric mean payoff games
Journal of Symbolic Computation
The level set method for the two-sided max-plus eigenproblem
Discrete Event Dynamic Systems
Playing games with scenario- and resource-aware SDF graphs through policy iteration
DATE '12 Proceedings of the Conference on Design, Automation and Test in Europe
A note on the approximation of mean-payoff games
Information Processing Letters
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Min-max functions are dynamic programming operators of zero-sum deterministic games with finite state and action spaces. The problem of computing the linear growth rate of the orbits (cycle-time) of a min-max function, which is equivalent to computing the value of a deterministic game with mean payoff, arises in the performance analysis of discrete event systems. We present here an improved version of the policy iteration algorithm given by Gaubert and Gunawardena in 1998 to compute the cycle-time of a min-max functions. The improvement consists of a fast evaluation of the spectral projector which is adapted to the case of large sparse graphs. We present detailed numerical experiments, both on randomly generated instances, and on concrete examples, indicating that the algorithm is experimentally fast.