Cyclic games and an algorithm to find minimax cycle means in directed graphs
USSR Computational Mathematics and Mathematical Physics
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
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
A survey of linear programming in randomized subexponential time
ACM SIGACT News
A subexponential randomized algorithm for the simple stochastic game problem
Information and Computation
The complexity of mean payoff games on graphs
Theoretical Computer Science
Theory of hybrid systems and discrete event systems
Theory of hybrid systems and discrete event systems
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
Infinite games on finitely coloured graphs with applications to automata on infinite trees
Theoretical Computer Science
Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
The random facet simplex algorithm on combinatorial cubes
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
A Discrete Subexponential Algorithm for Parity Games
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Small Progress Measures for Solving Parity Games
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
A Discrete Strategy Improvement Algorithm for Solving Parity Games
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
On Model-Checking for Fragments of µ-Calculus
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
CONCUR '95 Proceedings of the 6th International Conference on Concurrency Theory
A randomized subexponential algorithm for parity games
Nordic Journal of Computing
Unique Sink Orientations of Cubes
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Linear programming and unique sink orientations
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
An Optimal Strategy Improvement Algorithm for Solving Parity and Payoff Games
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Analytic Combinatorics
An Exponential Lower Bound for the Parity Game Strategy Improvement Algorithm as We Know it
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
A Deterministic Subexponential Algorithm for Solving Parity Games
SIAM Journal on Computing
Solving Parity Games in Practice
ATVA '09 Proceedings of the 7th International Symposium on Automated Technology for Verification and Analysis
The Complexity of Solving Stochastic Games on Graphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Discounted deterministic Markov decision processes and discounted all-pairs shortest paths
ACM Transactions on Algorithms (TALG)
Lower bounds for a subexponential optimization algorithm
Random Structures & Algorithms
Subexponential lower bounds for randomized pivoting rules for the simplex algorithm
Proceedings of the forty-third annual ACM symposium on Theory of computing
A subexponential lower bound for Zadeh's pivoting rule for solving linear programs and games
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Polynomial-Time algorithms for energy games with special weight structures
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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Parity Games form an intriguing family of infinite duration games whose solution is equivalent to the solution of important problems in automatic verification and automata theory. They also form a very natural subclass of Deterministic Mean Payoff Games, which in turn is a very natural subclass of turn-based Stochastic Mean Payoff Games. It is a major open problem whether these game families can be solved in polynomial time. The currently theoretically fastest algorithms for the solution of all these games are adaptations of the randomized algorithms of Kalai and of Matoušek, Sharir and Welzl for LP-type problems, an abstract generalization of linear programming. The expected running time of both algorithms is subexponential in the size of the game, i.e., 2O(√n log n), where n is the number of vertices in the game. We focus in this paper on the algorithm of Matoušek, Sharir and Welzl and refer to it as the Random Facet algorithm. Matoušek constructed a family of abstract optimization problems such that the expected running time of the Random Facet algorithm, when run on a random instance from this family, is close to the subexponential upper bound given above. This shows that in the abstract setting, the 2O(√n log n) upper bound on the complexity of the Random Facet algorithm is essentially tight. It is not known, however, whether the abstract optimization problems constructed by Matoušek correspond to games of any of the families mentioned above. There was some hope, therefore, that the Random Facet algorithm, when applied to, say, parity games, may run in polynomial time. We show, that this, unfortunately, is not the case by constructing explicit parity games on which the expected running time of the Random Facet algorithm is close to the subexponential upper bound. The games we use mimic the behavior of a randomized counter. They are also the first explicit LP-type problems on which the Random Facet algorithm is not polynomial.