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Zielonka's classic recursive algorithm for solving parity games is perhapsthe simplest among the many existing parity game algorithms. However, itscomplexity is exponential, while currently the state-of-the-art algorithms havequasipolynomial complexity. Here, we present a modification of Zielonka'sclassic algorithm that brings its complexity down to$n^{O\left(\log\left(1+\frac{d}{\log n}\right)\right)}$, for parity games ofsize $n$ with $d$ priorities, in line with previous quasipolynomial-timesolutions.

A Recursive Approach to Solving Parity Games in Quasipolynomial Time