Beyond Value Iteration for Parity Games - Strategy Iteration with Universal Trees

Explore a novel strategy iteration framework for parity games that builds upon universal trees. Delve into the challenges posed by quasi-polynomial algorithms since Calude et al.'s 2017 breakthrough, and understand the significance of universal trees as identified by Czerwiński et al. Learn how this new approach attempts to overcome the quasi-polynomial lower bound barrier on universal tree size. Examine the efficient method for computing least fixed points of operators associated with strategy subgraph arcs, adapted from shortest paths algorithms for ordered trees. Discover how this framework, when combined with existing universal tree structures, achieves competitive time complexities of O(mn2 log n log d) and O(mn2 log3 n log d) per iteration. Gain insights into the potential for surpassing current algorithmic limitations in solving parity games.