Attractors Is All You Need: Parity Games In Polynomial Time

TL;DR

This paper introduces a polynomial-time algorithm for solving parity games using a novel attractor method that guarantees finding the minimal dominion, ending a decades-long search in the field.

Contribution

It presents a new polynomial-time algorithm for parity games based on a unique attractor that only removes regions with a known winner, improving previous methods.

Findings

Algorithm runs in 7(n^{2} imes(n + m)) time

Guarantees finding the minimal dominion in parity games

Successfully peels the graph completely in polynomial time

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.