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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