Potts模型中条形晶格传输矩阵的多核计算
Multi-core computation of transfer matrices for strip lattices in the Potts model
摘要：
转移矩阵法是研究Potts模型中带状晶格的一种简便方法，因为计算代价只取决于晶格的周期部分，而不取决于整体。然而，即使当成本降低时，转移矩阵技术仍然是NP难问题，因为计算矩阵所需的时间T（|V|，|E|）作为图宽度的函数指数地增长。在这项工作中，我们提出了一个并行传输矩阵实现，多核架构下的性能扩展。矩阵的构造基于删除-收缩技术的几次重复，允许适合于多核机器的并行性。我们的实验结果表明，多核实现实现的加速比为3.7X与p = 4处理器和5.7X与p = 8。实现的效率介于60%和95%之间，在p = 4处理器的实际多核架构中实现了加速比和效率的最佳平衡。该算法还利用了晶格对称性，使传输矩阵计算比非对称计算快2倍，并使用原始空间的四分之一。
英文摘要：
The transfer-matrix technique is a convenient way for studying strip lattices in the Potts model since the compu- tational costs depend just on the periodic part of the lattice and not on the whole. However, even when the cost is reduced, the transfer-matrix technique is still an NP-hard problem since the time T(|V|, |E|) needed to compute the matrix grows ex- ponentially as a function of the graph width. In this work, we present a parallel transfer-matrix implementation that scales performance under multi-core architectures. The construction of the matrix is based on several repetitions of the deletion- contraction technique, allowing parallelism suitable to multi-core machines. Our experimental results show that the multi-core implementation achieves speedups of 3.7X with p = 4 processors and 5.7X with p = 8. The efficiency of the implementation lies between 60% and 95%, achieving the best balance of speedup and efficiency at p = 4 processors for actual multi-core architectures. The algorithm also takes advantage of the lattice symmetry, making the transfer matrix computation to run up to 2X faster than its non-symmetric counterpart and use up to a quarter of the original space.
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