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Accelerating Domain Propagation: an Efficient GPU-Parallel Algorithm over Sparse Matrices
arXiv - CS - Distributed, Parallel, and Cluster Computing Pub Date : 2020-09-16 , DOI: arxiv-2009.07785
Boro Sofranac, Ambros Gleixner, Sebastian Pokutta

Fast domain propagation of linear constraints has become a crucial component of today's best algorithms and solvers for mixed integer programming and pseudo-boolean optimization to achieve peak solving performance. Irregularities in the form of dynamic algorithmic behaviour, dependency structures, and sparsity patterns in the input data make efficient implementations of domain propagation on GPUs and, more generally, on parallel architectures challenging. This is one of the main reasons why domain propagation in state-of-the-art solvers is single thread only. In this paper, we present a new algorithm for domain propagation which (a) avoids these problems and allows for an efficient implementation on GPUs, and is (b) capable of running propagation rounds entirely on the GPU, without any need for synchronization or communication with the CPU. We present extensive computational results which demonstrate the effectiveness of our approach and show that ample speedups are possible on practically relevant problems: on state-of-the-art GPUs, our geometric mean speed-up for reasonably-large instances is around 10x to 20x and can be as high as 195x on favorably-large instances.

中文翻译:

加速域传播:稀疏矩阵上的高效 GPU 并行算法

线性约束的快速域传播已成为当今用于混合整数规划和伪布尔优化以实现峰值求解性能的最佳算法和求解器的重要组成部分。输入数据中动态算法行为、依赖结构和稀疏模式形式的不规则性使得在 GPU 上有效实现域传播,更一般地说,在并行架构上具有挑战性。这是最先进的求解器中域传播仅是单线程的主要原因之一。在本文中,我们提出了一种用于域传播的新算法,它 (a) 避免了这些问题并允许在 GPU 上有效实现,并且 (b) 能够完全在 GPU 上运行传播轮次,而无需任何同步或通信与 CPU。
更新日期:2020-09-21
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