Acceleration of Symmetric Sparse Matrix-Vector Product using Improved Hierarchical Diagonal Blocking Format

Abstract

In the previous study, Guy et al. proposed sparse matrix-vector product (SpMV) acceleration using the Hierarchical Diagonal Blocking (HDB) format that recursively repeated partitioning, reordering, and blocking on symmetric sparse matrix. The HDB format stores sparse matrix hierarchically using tree structure. Each node of tree structure of HDB format store small sparse matrices using CSR format. In this present study, we examined two problems with the HDB format and provided a solution for each problem. First, SpMV using the HDB format has a partial dependent relationship among hierarchies. The problem with the HDB format is that the parallelism of computation decreases as the hierarchy of nodes gets closer to the root. Thus, we propose cutting of dependency using work vectors to solve this problem. Second, each node of the conventional HDB format is stored in Compressed Sparse Row (CSR) format. Block compressed Sparse Row (BSR) format often becomes faster than CSR format in SpMV performance. Thus, we evaluated the effectiveness of our proposed method with work vectors also for BSR-HDB format. In addition, we compare the performance in the general format (CSR format, BSR format) using the Intel Math Kernel Library (MKL), the conventional HDB format, and the expanded HDB format by using 22 types of sparse matrix that from various field. The results showed that the SpMV performance was highest in the HDB format that we expanded in 19 types of sparse matrix, which was 1.99 times faster than the CSR format.