Efficient Parallel Scheduling for Sparse Triangular Solvers
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910988166496256 |
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| author | Böhnlein, Toni Papp, Pál András Steiner, Raphael S. Matzoros, Christos K. Yzelman, A. N. |
| author_facet | Böhnlein, Toni Papp, Pál András Steiner, Raphael S. Matzoros, Christos K. Yzelman, A. N. |
| contents | We develop and analyze new scheduling algorithms for solving sparse triangular linear systems (SpTRSV) in parallel. Our approach produces highly efficient synchronous schedules for the forward- and backward-substitution algorithm. Compared to state-of-the-art baselines HDagg and SpMP, we achieve a $3.32 \times$ and $1.42 \times$ geometric-mean speed-up, respectively. We achieve this by obtaining an up to $12.07 \times$ geometric-mean reduction in the number of synchronization barriers over HDagg, whilst maintaining a balanced workload, and by applying a matrix reordering step for locality. We show that our improvements are consistent across a variety of input matrices and hardware architectures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_05408 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient Parallel Scheduling for Sparse Triangular Solvers Böhnlein, Toni Papp, Pál András Steiner, Raphael S. Matzoros, Christos K. Yzelman, A. N. Distributed, Parallel, and Cluster Computing 68W10, 65F50 C.1.4; G.1.3 We develop and analyze new scheduling algorithms for solving sparse triangular linear systems (SpTRSV) in parallel. Our approach produces highly efficient synchronous schedules for the forward- and backward-substitution algorithm. Compared to state-of-the-art baselines HDagg and SpMP, we achieve a $3.32 \times$ and $1.42 \times$ geometric-mean speed-up, respectively. We achieve this by obtaining an up to $12.07 \times$ geometric-mean reduction in the number of synchronization barriers over HDagg, whilst maintaining a balanced workload, and by applying a matrix reordering step for locality. We show that our improvements are consistent across a variety of input matrices and hardware architectures. |
| title | Efficient Parallel Scheduling for Sparse Triangular Solvers |
| topic | Distributed, Parallel, and Cluster Computing 68W10, 65F50 C.1.4; G.1.3 |
| url | https://arxiv.org/abs/2503.05408 |