发表机构
University of Yamanashi（山梨大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究对比ICCG方法并行预处理中，需预先指定块数的ABMC方法与自动生成块的Leiden方法，发现采用常数Potts模型的Leiden方法性能可与优化块数的ABMC相当。
AI 中文摘要
在不完全乔列斯基预处理应用于不完全乔列斯基-共轭梯度（ICCG）方法时，前向和后向替换存在顺序依赖，这是多核环境下并行化的主要瓶颈。为缓解该瓶颈，代数块多着色（ABMC）方法通过分块着色实现了并行性与数据局部性，但ABMC需预先指定块数作为输入参数。本研究评估Leiden方法作为ICCG方法并行预处理的替代分块 approach，Leiden是最大化图划分质量函数的社区检测技术，可自动生成反映矩阵结构的块，无需预先确定块数。我们使用Leiden方法划分稀疏矩阵的邻接图，并将所得块用于并行预处理；以模块度和常数Potts模型作为质量函数实现Leiden方法，在8个对称正定矩阵上，从迭代次数、执行时间和L2缓存效率三个方面，将其性能与ABMC方法对比。实验结果表明，采用常数Potts模型的Leiden方法，其性能可与配置了优化块数的ABMC方法相当。
英文摘要
In the application of incomplete Cholesky preconditioning to the incomplete Cholesky-conjugate gradient (ICCG) method, forward and backward substitutions exhibit sequential dependencies that constitute a major bottleneck for parallelization in multicore environments. To alleviate this bottleneck, the algebraic block multi-coloring (ABMC) method achieves both parallelism and data locality through block-wise coloring. However, ABMC requires the number of blocks to be specified as an input parameter in advance. This study evaluates the Leiden method as an alternative blocking approach for parallel preconditioning in the ICCG method. As a community detection technique that maximizes a quality function for graph partitioning, the Leiden method automatically generates blocks that reflect the matrix structure without requiring the number of blocks a priori. We partition the adjacency graphs of sparse matrices using the Leiden method and utilize the resulting blocks for parallel preconditioning. We implement the Leiden method using modularity and the constant Potts model as quality functions and compare its performance with that of the ABMC method in terms of the number of iterations, execution time, and L2 cache efficiency across eight symmetric positive definite matrices. The experimental results demonstrate that the Leiden method with the constant Potts model achieves performance comparable to that of the ABMC method configured with an optimized number of blocks.
