Mean-payoff parity games in quasipolynomial time

We give a uniform deterministic quasipolynomial-time algorithm for mean-payoff parity games. It computes all vertices from which a player can enforce both nonnegative liminf mean payoff and the parity condition, with arbitrary signed binary rewards and unrestricted binary priorities. The running time is $2^{O((\log (L+2){)}^2)}$ bit operations, where L is the complete input length.