The existence of polynomial time algorithms for the solution of parity games is a major open problem. The fastest known algorithms for the problem are randomized algorithms that run in subexponential time. Randomness seems to play an essential role in these algorithms. We use a completely different, and elementary, approach to obtain a deterministic subexponential algorithm for the solution of parity games. Our deterministic algorithm is almost as fast as the randomized algorithms mentioned above.
This is joint work with Mike Paterson and Uri Zwick.