Attractors Is All You Need: Parity Games In Polynomial Time

Rick van der Heijden

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arXiv · 2511.03752

Attractors Is All You Need: Parity Games In Polynomial Time

Rick van der Heijden

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Abstract

This paper provides a polynomial-time algorithm for solving parity games that runs in $\mathcal{O}(n^{2}\cdot(n + m))$ time-ending a search that has taken decades. Unlike previous attractor-based algorithms, the presented algorithm only removes regions with a determined winner. The paper introduces a new type of attractor that can guarantee finding the minimal dominion of a parity game. The attractor runs in polynomial time and can peel the graph empty.

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Rick van der Heijden. 2025-11-04. Attractors Is All You Need: Parity Games In Polynomial Time. https://arxiv.org/abs/2511.03752

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