Modeling the consumption of limited resources, e.g., time or energy, plays a central role on the design of reactive systems such as embedded controllers. To this aim, quantitative objectives are defined on game arenas that can be easily modeled as weighted graphs. Instances of these games, called energy games , can be solved in ${\mathcal {O}(\vert {E}\vert {\cdot }\vert {V}\vert {\cdot }W)}$ where $W$ is the maximum weight. Recent work has demonstrated that sequential implementations hardly solve practical instances due to their size and the number of interactions required to converge to a solution. Recent work has demonstrated that sequential implementations hardly solve practical instances. Furthermore, emerging approaches, that have investigated the parallelism of CPUs multi-core and GPU for solving the initial credit problem for energy games, still perform poorly due to the non-trivial characteristics of these graphs. In this article we first describe a revised version of the algorithm on multi-core CPU that obtains a faster convergence time on real-world graphs with up to 30x against the serial implementation by showing good scalability overall. Second, we provide a new GPU-based parallel implementation based on warp-level primitives that allows to reduce the time-to-solution on several instances with up to 3.6x of speed-up against traditional parallel vertex-based approaches. We also discuss a methodology to build synthetic energy games to validate the scalability of parallel algorithms on two totally different settings.

中文翻译：

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GPU 上的可扩展能量游戏求解器

对有限资源（例如时间或能量）的消耗进行建模在反应系统（例如嵌入式控制器）的设计中起着核心作用。为此，在游戏领域定义了量化目标，可以轻松地将其建模为加权图。这些游戏的实例，称为能量游戏 , 可以求解 ${\mathcal {O}(\vert {E}\vert {\cdot }\vert {V}\vert {\cdot }W)}$ 在哪里 $W$是最大重量。最近的工作表明，顺序实现很难解决实际实例，因为它们的大小和收敛到解决方案所需的交互数量。最近的工作表明，顺序实现很难解决实际情况。此外，新兴的方法已经研究了 CPU 多核和 GPU 的并行性，以解决初始信用问题对于能量游戏，由于这些图的非平凡特征，仍然表现不佳。在本文中，我们首先描述了多核 CPU 上算法的修订版本，该版本通过显示出良好的整体可扩展性，在真实世界图上获得了更快的收敛时间，与串行实现相比最高可达 30 倍。其次，我们提供了一种基于扭曲级原语的新的基于 GPU 的并行实现，与传统的基于并行顶点的方法相比，它可以减少多个实例的求解时间，速度提高高达 3.6 倍。我们还讨论了一种构建合成能量游戏的方法，以验证并行算法在两种完全不同的设置下的可扩展性。