A Recursive Approach to Solving Parity Games in Quasipolynomial Time

TL;DR

This paper introduces a modified recursive algorithm for solving parity games that achieves quasipolynomial time complexity, aligning with the efficiency of the best existing algorithms.

Contribution

The authors adapt Zielonka's classic recursive algorithm to operate in quasipolynomial time, improving its practical applicability for large parity games.

Findings

Achieves quasipolynomial complexity for parity games

Maintains simplicity of Zielonka's recursive approach

Bridges gap between classic and modern algorithms

Abstract

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.