Simple stochastic games with few random vertices are easy to solve

Authors:
Hugo Gimbert;Florian Horn
Affiliations:
LaBRI, Université Bordeaux 1, France;LIAFA, Université Paris 7, France
Venue:
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Year:
2008

Citing 6
Cited 8

A polynomial-time algorithm, based on Newton's method, for linear programming

Mathematical Programming: Series A and B
The complexity of stochastic games

Information and Computation
A subexponential randomized algorithm for the simple stochastic game problem

Information and Computation
Finite State Markovian Decision Processes

Finite State Markovian Decision Processes
Simple Stochastic Games, Parity Games, Mean Payoff Games and Discounted Payoff Games Are All LP-Type Problems

Algorithmica
New Algorithms for Solving Simple Stochastic Games

Electronic Notes in Theoretical Computer Science (ENTCS)

Termination criteria for solving concurrent safety and reachability games

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
The Complexity of Solving Stochastic Games on Graphs

ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Qualitative concurrent parity games

ACM Transactions on Computational Logic (TOCL)
Automatizability and simple stochastic games

ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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
Solving simple stochastic games with few coin toss positions

ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Strategy improvement for concurrent reachability and turn-based stochastic safety games

Journal of Computer and System Sciences
A pseudo-polynomial algorithm for mean payoff stochastic games with perfect information and a few random positions

ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a new algorithm for solving Simple Stochastic Games (SSGs). This algorithm is based on an exhaustive search of a special kind of positional optimal strategies, the f-strategies. The running time is O( |VR|! ċ (|V ||E| + |p|) ), where |V |, |VR|, |E| and |p| are respectively the number of vertices, random vertices and edges, and the maximum bit-length of a transition probability. Our algorithm improves existing algorithms for solving SSGs in three aspects. First, our algorithm performs well on SSGs with few random vertices, second it does not rely on linear or quadratic programming, third it applies to all SSGs, not only stopping SSGs.