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Efficient Block Algorithms for Parallel Sparse Triangular Solve

Authors:

Weifeng LiuAuthors Info & Claims

ICPP '20: Proceedings of the 49th International Conference on Parallel Processing

Article No.: 63, Pages 1 - 11

https://doi.org/10.1145/3404397.3404413

Published: 17 August 2020 Publication History

Abstract

The sparse triangular solve (SpTRSV) kernel is an important building block for a number of linear algebra routines such as sparse direct and iterative solvers. The major challenge of accelerating SpTRSV lies in the difficulties of finding higher parallelism. Existing work mainly focuses on reducing dependencies and synchronizations in the level-set methods. However, the 2D block layout of the input matrix has been largely ignored in designing more efficient SpTRSV algorithms.

In this paper, we implement three block algorithms, i.e., column block, row block and recursive block algorithms, for parallel SpTRSV on modern GPUs, and propose an adaptive approach that can automatically select the best kernels according to input sparsity structures. By testing 159 sparse matrices on two high-end NVIDIA GPUs, the experimental results demonstrate that the recursive block algorithm has the best performance among the three block algorithms, and it is on average 4.72x (up to 72.03x) and 9.95x (up to 61.08x) faster than cuSPARSE v2 and Sync-free methods, respectively. Besides, our method merely needs moderate cost for preprocessing the input matrix, thus is highly efficient for multiple right-hand sides and iterative scenarios.

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Hu ZSun JLi ZSun G(2024)AG-SpTRSV: An Automatic Framework to Optimize Sparse Triangular Solve on GPUsACM Transactions on Architecture and Code Optimization10.1145/367491121:4(1-25)Online publication date: 25-Jun-2024
https://dl.acm.org/doi/10.1145/3674911
He ZSong LLucas RCong JZhang ZPutnam A(2024)LevelST: Stream-based Accelerator for Sparse Triangular SolverProceedings of the 2024 ACM/SIGDA International Symposium on Field Programmable Gate Arrays10.1145/3626202.3637568(67-77)Online publication date: 1-Apr-2024
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Freire MDufrechou EEzzatti P(2024)A new level-set analysis and sparse storage format for the SPTRSV in GPUs2024 IEEE 36th International Symposium on Computer Architecture and High Performance Computing (SBAC-PAD)10.1109/SBAC-PAD63648.2024.00014(59-69)Online publication date: 13-Nov-2024
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ICPP '20: Proceedings of the 49th International Conference on Parallel Processing

August 2020

844 pages

ISBN:9781450388160

DOI:10.1145/3404397

Copyright © 2020 ACM.

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ICPP '20: 49th International Conference on Parallel Processing

August 17 - 20, 2020

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https://dl.acm.org/doi/10.1145/3674911
He ZSong LLucas RCong JZhang ZPutnam A(2024)LevelST: Stream-based Accelerator for Sparse Triangular SolverProceedings of the 2024 ACM/SIGDA International Symposium on Field Programmable Gate Arrays10.1145/3626202.3637568(67-77)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1145/3626202.3637568
Freire MDufrechou EEzzatti P(2024)A new level-set analysis and sparse storage format for the SPTRSV in GPUs2024 IEEE 36th International Symposium on Computer Architecture and High Performance Computing (SBAC-PAD)10.1109/SBAC-PAD63648.2024.00014(59-69)Online publication date: 13-Nov-2024
https://doi.org/10.1109/SBAC-PAD63648.2024.00014
Baek DHwang SHuh J(2024)pSyncPIM: Partially Synchronous Execution of Sparse Matrix Operations for All-Bank PIM Architectures2024 ACM/IEEE 51st Annual International Symposium on Computer Architecture (ISCA)10.1109/ISCA59077.2024.00034(354-367)Online publication date: 29-Jun-2024
https://doi.org/10.1109/ISCA59077.2024.00034
Ji JGuo JFan X(2023)Design and Implementation of a Parallel Algorithm for Solving Linear Equations Using Gaussian Elimination MethodProceedings of the 2023 7th International Conference on Electronic Information Technology and Computer Engineering10.1145/3650400.3650588(1114-1118)Online publication date: 20-Oct-2023
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Lu ZLiu W(2023)TileSpTRSV: a tiled algorithm for parallel sparse triangular solve on GPUsCCF Transactions on High Performance Computing10.1007/s42514-023-00151-15:2(129-143)Online publication date: 12-Jun-2023
https://doi.org/10.1007/s42514-023-00151-1
Li JLiang JXue WHu ZLi LShi J(2023)Toward efficient structured-grid triangular solver on sunway many-core processorsThe Journal of Supercomputing10.1007/s11227-023-05802-280:8(10610-10636)Online publication date: 27-Dec-2023
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Niu YLu ZJi HSong SJin ZLiu WLee JAgrawal KSpear M(2022)TileSpGEMMProceedings of the 27th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming10.1145/3503221.3508431(90-106)Online publication date: 2-Apr-2022
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Tian MWang JZhang ZDu WPan JLiu T(2022)swSuperLU: A highly scalable sparse direct solver on Sunway manycore architectureThe Journal of Supercomputing10.1007/s11227-021-04270-w78:9(11441-11463)Online publication date: 1-Jun-2022
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Ahmad NYilmaz BUnat D(2021)A Split Execution Model for SpTRSVIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2021.307450132:11(2809-2822)Online publication date: 1-Nov-2021
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