A General Optimization Method for SpMV Based on Graph Partitioning and Matrix Reordering

With the rising demand for the performance of sparse matrix-vector multiplication (SpMV) in various fields, traditional optimization approaches for SpMV computation, which are designed specifically for certain domains, encounter the issue of limited data applicability. Moreover, as SpMV computation is memory-access intensive, the inefficiency of vector memory access emerges as a significant performance bottleneck. This paper proposes a comprehensive optimization scheme integrating graph partitioning and matrix reordering techniques. By transforming the sparse matrix into a graph and performing partitioning and reordering, the distribution of nonzero elements is effectively changed, the memory access order is adjusted, and the data locality is significantly improved, thereby enhancing the memory access efficiency and overall computational performance. Experimental results show that this method successfully increases the sparsity within the diagonal range by an average of 9.51 times, and the average speedup ratio of the overall SpMV computation on the CPU reaches 1.26, demonstrating strong versatility and laying a solid foundation for the efficient application of SpMV in multiple fields.