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