Efficient Parallel Strategy Improvement for Parity Games

John Fearnley
Department of Computer Science, University of Liverpool, UK
arXiv:1705.02313 [cs.DS], (5 May 2017)


   title={Efficient Parallel Strategy Improvement for Parity Games},

   author={Fearnley, John},






We study strategy improvement algorithms for solving parity games. While these algorithms are known to solve parity games using a very small number of iterations, experimental studies have found that a high step complexity causes them to perform poorly in practice. In this paper we seek to address this situation. Every iteration of the algorithm must compute a best response, and while the standard way of doing this uses the Bellman-Ford algorithm, we give experimental results that show that one-player strategy improvement significantly outperforms this technique in practice. We then study the best way to implement one-player strategy improvement, and we develop an efficient parallel algorithm for carrying out this task, by reducing the problem to computing prefix sums on a linked list. We report experimental results for these algorithms, and we find that a GPU implementation of this algorithm shows a significant speedup over single-core and multi-core CPU implementations.
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