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Communication Dans Un Congrès Année : 2022

Tight Memory-Independent Parallel Matrix Multiplication Communication Lower Bounds

Résumé

Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored the constant factors or not obtained the tightest possible values. Recent work has demonstrated that more careful analysis improves the best known constants for some classical matrix multiplication lower bounds and helps to identify more efficient algorithms that match the leading-order terms in the lower bounds exactly and improve practical performance. The main result of this work is the establishment of 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 aspect ratios of the matrices.
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Dates et versions

hal-03950351 , version 1 (21-01-2023)

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Hussam Al Daas, Grey Ballard, Laura Grigori, Suraj Kumar, Kathryn Rouse. Tight Memory-Independent Parallel Matrix Multiplication Communication Lower Bounds. SPAA 2022 - 34th ACM Symposium on Parallelism in Algorithms and Architectures, Jul 2022, Philadelphia PA, United States. ⟨10.1145/3490148.3538552⟩. ⟨hal-03950351⟩
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