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 subexponential randomized algorithm for the simple stochastic game problem
Information and Computation
The complexity of mean payoff games on graphs
Theoretical Computer Science
Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
A Discrete Subexponential Algorithm for Parity Games
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
A subexponential lower bound for the random facet algorithm for parity games
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We describe a randomized algorithm for Parity Games (equivalent to the Mu-Calculus Model Checking), which runs in expected time 2O(k1/(1+2epsilon)) when k is Omega(n1/2+epsilon), n is the number of vertices, and 0 epsilon = 1/2. That is, our algorithm is subexponential in the number of colors k of the game graph provided that k is not too small. All previously known algorithms were exponential in the number of colors, with the best one taking time and space O(k2 n sqrt(n)k). Our algorithm does not rely on Linear Programming subroutines and uses a low-degree polynomial space.