Spatiotemporal Graph and Hypergraph Partitioning Models for Sparse Matrix-Vector Multiplication on Many-Core Architectures

Abubaker, Nabil; Akbudak, Kadir; Aykanat, Cevdet

doi:10.1109/tpds.2018.2864729

Cited by 9 publications

(3 citation statements)

References 30 publications

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“…Adaptive optimization methods of SpMV based on machine learning techniques have attracted interests in recent years [15,[36][37][38][39][40][41]. This is due to the fact that the SpMV performance is determined by a combination of the storage format, the platform architecture, and the input dataset.…”

Section: Related Workmentioning

confidence: 99%

Adaptive Hybrid Storage Format for Sparse Matrix–Vector Multiplication on Multi-Core SIMD CPUs

Chen

Fang

et al. 2022

Applied Sciences

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Optimizing sparse matrix–vector multiplication (SpMV) is challenging due to the non-uniform distribution of the non-zero elements of the sparse matrix. The best-performing SpMV format changes depending on the input matrix and the underlying architecture, and there is no “one-size-fit-for-all” format. A hybrid scheme combining multiple SpMV storage formats allows one to choose an appropriate format to use for the target matrix and hardware. However, existing hybrid approaches are inadequate for utilizing the SIMD cores of modern multi-core CPUs with SIMDs, and it remains unclear how to best mix different SpMV formats for a given matrix. This paper presents a new hybrid storage format for sparse matrices, specifically targeting multi-core CPUs with SIMDs. Our approach partitions the target sparse matrix into two segmentations based on the regularities of the memory access pattern, where each segmentation is stored in a format suitable for its memory access patterns. Unlike prior hybrid storage schemes that rely on the user to determine the data partition among storage formats, we employ machine learning to build a predictive model to automatically determine the partition threshold on a per matrix basis. Our predictive model is first trained off line, and the trained model can be applied to any new, unseen sparse matrix. We apply our approach to 956 matrices and evaluate its performance on three distinct multi-core CPU platforms: a 72-core Intel Knights Landing (KNL) CPU, a 128-core AMD EPYC CPU, and a 64-core Phytium ARMv8 CPU. Experimental results show that our hybrid scheme, combined with the predictive model, outperforms the best-performing alternative by 2.9%, 17.5% and 16% on average on KNL, AMD, and Phytium, respectively.

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Section: Related Workmentioning

confidence: 99%

Adaptive Hybrid Storage Format for Sparse Matrix–Vector Multiplication on Multi-Core SIMD CPUs

Chen

Fang

et al. 2022

Applied Sciences

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“…General sparse matrix-matrix multiplication is a basic operation in the sparse matrix, which is widely used in various scientific and engineering applications, such as AMG(algebraic multi-grid) [2,18], multi-source breadth-first search [3], bioinformatics [10], multi-source shortest path [4], machine learning [11,16,17]. First, the mathematical model was established based on partial differential equations, and then we solve partial differential equations with the finite element and finite volume method and form large-scale sparse linear equations [1,9].…”

Section: Introductionmentioning

confidence: 99%

SPMSD: An Partitioning-Strategy for Parallel General Sparse Matrix-Matrix Multiplication on GPU

Cui,

Wang,

Han

et al. 2024

Parallel Process. Lett.

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SpGEMM (General Sparse Matrix-Matrix Multiplication) is one of the kernels of an algebraic multi-grid method, graph algorithm, and solving linear equations. Due to the non-uniformity of some sparse matrices, the existing parallel SpGEMM algorithms suffer from load imbalance, lead to a decrease in computational efficiency. This paper proposes a new algorithm, SPMSD (SpGEMM Based on Minimum Standard Deviation). The algorithm is developed based on a hash table and partition strategy. First, the number of intermediate results in the matrix is divided into multiple blocks based on a new partition strategy to ensure the minimum standard deviation among blocks. Second, the input matrix is transformed according to the result of the partition strategy. Finally, SPMSD performs the parallel computing of SpGEMM based on the advantages of fast insertion and also fast access storage of the hash table and the calculation process controls the insertion and merging of intermediate results according to the offset to avoid the shortage of atomic operations. These experiments indicate the execution of SPMSD is faster than the existing cuSPARSE libraries by 7.4x. Compared with the Out of Core method, SPMSD improves the computational performance by 1.2x, SPMSD memory utilization is decreased by 0.19x.

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Section: Introductionmentioning

confidence: 99%

SPMSD: An Partitioning-Strategy for Parallel General Sparse Matrix-Matrix Multiplication on GPU

Cui

wang

Han

et al. 2022

Preprint

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SpGEMM (General Sparse Matrix-Matrix Multiplication) is one of the kernels of an algebraic multi-grid method, graph algorithm, and solving linear equations. Due to the non-uniformity of some sparse matrices, the existing parallel SpGEMM algorithms suffer from load imbalance, which will lead to a decrease in computational efficiency. This paper proposes a new algorithm, SPMSD (SpGEMM Based on Minimum Standard Deviation). The algorithm is developed based on a hash table and partition strategy. First, the number of intermediate results in each row of matrix is divided into multiple blocks based on a new partition strategy to ensure the minimum standard deviation among blocks. Second, the input matrix is transformed according to the result of the partition strategy. Finally, SPMSD performs the parallel computation of SpGEMM based on the advantages of fast insertion and also fast access storage of hash table and the calculation process controls the insertion and merging of intermediate results according to the offset to avoid the shortage of atomic operations. The model of the GPU graphics card used in the experiment is NVIDIA Tesla V100 with 5120 cores. These experiments indicate the execution of SPMSD is faster than the existing cuSPARSE libraries by 7.4x. Compared with the Out of Core method, SPMSD improves the computational performance by 1.2x and memory utilization decreased by 0.19x. In summary, the algorithm proposed in this paper further improves the parallel computing efficiency of SpGEMM to an extent.

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Spatiotemporal Graph and Hypergraph Partitioning Models for Sparse Matrix-Vector Multiplication on Many-Core Architectures

Cited by 9 publications

References 30 publications

Adaptive Hybrid Storage Format for Sparse Matrix–Vector Multiplication on Multi-Core SIMD CPUs

Adaptive Hybrid Storage Format for Sparse Matrix–Vector Multiplication on Multi-Core SIMD CPUs

SPMSD: An Partitioning-Strategy for Parallel General Sparse Matrix-Matrix Multiplication on GPU

SPMSD: An Partitioning-Strategy for Parallel General Sparse Matrix-Matrix Multiplication on GPU

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