Balancing Computation and Communication in Distributed Sparse Matrix-Vector Multiplication

Abstract

Sparse Matrix-Vector Multiplication (SpMV) is a fundamental operation in a number of scientific and engineering problems. When the sparse matrices processed are large enough, distributed memory systems should be used to accelerate SpMV. At present, the optimization techniques for distributed SpMV mainly focus on reordering through graph or hypergraph partitioning. However, although the reordering could reduce the amount of communications in general, there are still load balancing challenges in computations and communications on distributed platforms that are not well addressed. In this paper, we propose two strategies to optimize SpMV on distributed clusters: (1) resizing the number of row blocks on the nodes for balancing the amount of computations, and (2) adjusting the column number of the diagonal blocks for balancing tasks and reducing communications among compute nodes. The experimental results show that compared with the classic distributed SpMV implementation and its variant reordered with graph partitioning, our algorithm achieves on average 77.20x and 5.18x (up to 460.52x and 27.50x) speedups, respectively. Also, our method bring on average 19.56x (up to 48.49x) speedup over a recently proposed hybrid distributed SpMV algorithm. In addition, our algorithm achieves obviously better scalability over these existing distributed SpMV methods.