简短公告:紧内存无关并行矩阵乘法通信下界

Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures Pub Date : 2022-05-26 DOI:10.1145/3490148.3538552

Hussam Al Daas, Grey Ballard, L. Grigori, Suraj Kumar, Kathryn Rouse

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引用次数: 3

摘要

对于矩阵乘法算法，通信下界早已建立。然而，大多数渐近分析方法要么忽略了常数因素，要么没有得到最接近的可能值。这项工作的主要结果是建立了具有紧常数的并行矩阵乘法的与内存无关的通信下界。在依赖于矩阵长宽比和处理器数量的相对大小的三种情况下，我们的常数都比以前的工作有所改进。

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Brief Announcement: Tight Memory-Independent Parallel Matrix Multiplication Communication Lower Bounds

Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored constant factors or not obtained the tightest possible values. The main result of this work is establishing memory-independent communication lower bounds with tight constants for parallel matrix multiplication. Our constants improve on previous work in each of three cases that depend on the relative sizes of the matrix aspect ratios and the number of processors.

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Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures

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