In this work, we perform the feasibility analysis of a multi‐grained parallel version of the Zielonka Recursive (ZR) algorithm exploiting the coarse‐ and fine‐ grained concurrency. Coarse‐grained parallelism relies on a suitable splitting of the problem, that is, a graph decomposition based on its Strongly Connected Components (SCC) or a splitting of the formula generating the game, while fine‐grained parallelism is introduced inside the Attractor which is the most intensive computational kernel. This configuration is new and addressed for the first time in this article. Innovation goes from the introduction of properly defined metrics for the strong and weak scaling of the algorithm. These metrics conduct to an analysis of the values of these metrics for the fine grained algorithm, we can infer the expected performance of the multi‐grained parallel algorithm running in a distributed and hybrid computing environment. Results confirm that while a fine‐grained parallelism have a clear performance limitation, the performance gain we can expect to get by employing a multilevel parallelism is significant.

中文翻译：

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解决奇偶游戏的多级可扩展并行 Zielonka 算法

在这项工作中，我们对利用粗粒度和细粒度并发性的 Zielonka 递归 (ZR) 算法的多粒度并行版本进行了可行性分析。粗粒度并行依赖于对问题的适当拆分，即基于其强连接组件（SCC）的图分解或生成博弈的公式的拆分，而细粒度并行则是在 Attractor 内部引入的最密集的计算内核。此配置是新的，并在本文中首次解决。创新源于为算法的强弱缩放引入了正确定义的度量。这些指标用于分析细粒度算法的这些指标的值，我们可以推断在分布式和混合计算环境中运行的多粒度并行算法的预期性能。结果证实，虽然细粒度并行具有明显的性能限制，但我们通过采用多级并行可以获得显着的性能提升。