Distributed-Memory Parallel Algorithms for Sparse Matrix and Sparse Tall-and-Skinny Matrix Multiplication
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arXiv
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| Format: | Preprint |
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2024
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| author | Ranawaka, Isuru Hussain, Md Taufique Block, Charles Gerogiannis, Gerasimos Torrellas, Josep Azad, Ariful |
| author_facet | Ranawaka, Isuru Hussain, Md Taufique Block, Charles Gerogiannis, Gerasimos Torrellas, Josep Azad, Ariful |
| contents | We consider a sparse matrix-matrix multiplication (SpGEMM) setting where one matrix is square and the other is tall and skinny. This special variant, called TS-SpGEMM, has important applications in multi-source breadth-first search, influence maximization, sparse graph embedding, and algebraic multigrid solvers. Unfortunately, popular distributed algorithms like sparse SUMMA deliver suboptimal performance for TS-SpGEMM. To address this limitation, we develop a novel distributed-memory algorithm tailored for TS-SpGEMM. Our approach employs customized 1D partitioning for all matrices involved and leverages sparsity-aware tiling for efficient data transfers. In addition, it minimizes communication overhead by incorporating both local and remote computations. On average, our TS-SpGEMM algorithm attains 5x performance gains over 2D and 3D SUMMA. Furthermore, we use our algorithm to implement multi-source breadth-first search and sparse graph embedding algorithms and demonstrate their scalability up to 512 Nodes (or 65,536 cores) on NERSC Perlmutter. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_11988 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributed-Memory Parallel Algorithms for Sparse Matrix and Sparse Tall-and-Skinny Matrix Multiplication Ranawaka, Isuru Hussain, Md Taufique Block, Charles Gerogiannis, Gerasimos Torrellas, Josep Azad, Ariful Distributed, Parallel, and Cluster Computing We consider a sparse matrix-matrix multiplication (SpGEMM) setting where one matrix is square and the other is tall and skinny. This special variant, called TS-SpGEMM, has important applications in multi-source breadth-first search, influence maximization, sparse graph embedding, and algebraic multigrid solvers. Unfortunately, popular distributed algorithms like sparse SUMMA deliver suboptimal performance for TS-SpGEMM. To address this limitation, we develop a novel distributed-memory algorithm tailored for TS-SpGEMM. Our approach employs customized 1D partitioning for all matrices involved and leverages sparsity-aware tiling for efficient data transfers. In addition, it minimizes communication overhead by incorporating both local and remote computations. On average, our TS-SpGEMM algorithm attains 5x performance gains over 2D and 3D SUMMA. Furthermore, we use our algorithm to implement multi-source breadth-first search and sparse graph embedding algorithms and demonstrate their scalability up to 512 Nodes (or 65,536 cores) on NERSC Perlmutter. |
| title | Distributed-Memory Parallel Algorithms for Sparse Matrix and Sparse Tall-and-Skinny Matrix Multiplication |
| topic | Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2408.11988 |