Communication-Avoiding Parallel Sparse-Dense Matrix-Matrix Multiplication
| Autor: | Katherine Yelick, Leonid Oliker, Ariful Azad, Aydin Buluc, Sang-Yun Oh, Penporn Koanantakool, Dmitriy Morozov |
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| Rok vydání: | 2016 |
| Předmět: |
Multiplication algorithm
Matrix-free methods Band matrix Computer science Parallel algorithm Block matrix 010103 numerical & computational mathematics Parallel computing Sparse approximation 01 natural sciences Matrix chain multiplication Matrix multiplication Matrix decomposition 010104 statistics & probability Cuthill–McKee algorithm Linear algebra Multiplication Algorithm design 0101 mathematics Sparse matrix |
| Zdroj: | IPDPS |
| DOI: | 10.1109/ipdps.2016.117 |
| Popis: | Multiplication of a sparse matrix with a dense matrix is a building block of an increasing number of applications in many areas such as machine learning and graph algorithms. However, most previous work on parallel matrix multiplication considered only both dense or both sparse matrix operands. This paper analyzes the communication lower bounds and compares the communication costs of various classic parallel algorithms in the context of sparse-dense matrix-matrix multiplication. We also present new communication-avoiding algorithms based on a 1D decomposition, called 1.5D, which -- while suboptimal in dense-dense and sparse-sparse cases -- outperform the 2D and 3D variants both theoretically and in practice for sparse-dense multiplication. Our analysis separates one-time costs from per iteration costs in an iterative machine learning context. Experiments demonstrate speedups up to 100x over a baseline 3D SUMMA implementation and show parallel scaling over 10 thousand cores. |
| Databáze: | OpenAIRE |
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