A Conflict-aware Divide-and-Conquer Algorithm for Symmetric Sparse Matrix-Vector Multiplication

Haozhong Qiu, Chuanfu Xu, Jianbin Fang, Jian Zhang, Liang Deng, Yue Ding, Qingsong Wang, Shizhao Chen, Yonggang Che, Jie Liu

Abstract: Exploiting matrix symmetry to halve memory footprint offers an opportunity for accelerating memory-bound computations like Sparse Matrix-Vector Multiplication (SpMV). However, symmetric SpMV incurs data conflicts when concurrently writing the output vector. Previous approaches fail to address this issue efficiently. This paper proposes DCS-SpMV, a Divide-and-Conquer (DC) algorithm for efficient Symmetric SpMV. The key idea is to recursively divide the matrix-induced conflict graph into independent subgraphs for parallel execution, and construct separate subgraphs to avoid data conflicts. Our DC algorithm transforms the input matrix into a low-conflict part and a high-conflict part, which motivates us to design a conflict-aware hybrid solution that executes these two parts using DCS-SpMV and traditional SpMV respectively. We develop a machine learning model to predict an optimal hybrid implementation for a given matrix and architecture. We evaluate our work on both X86 and ARM CPUs, demonstrating significant performance improvement over the state-of-the-art.