Segmented Operations for Sparse Matrix Computation on Vector Multiprocessors

In this paper we present a new technique for sparse matrix multiplication on vector multiprocessors based on the efficient implementation of a segmented sum operation. We describe how the segmented sum can be implemented on vector multiprocessors such that it both fully vectorizes within each processor and parallelizes across processors. Because of our method’s insensitivity to relative row size, it is better suited than the Ellpack/Itpack or the Jagged Diagonal algorithms for matrices which have a varying number of non-zero elements in each row. Furthermore, our approach requires less preprocessing (no more time than a single sparse matrix-vector multiplication), less auxiliary storage, and uses a more convenient data representation (an augmented form of the standard compressed sparse row format). We have implemented our algorithm (SEGMV) on the Cray Y-MP C90, and have compared its performance with other methods on a variety of sparse matrices from the Harwell-Boeing collection and industrial application codes. Our performance on the test matrices is up to 3 times faster than the Jagged Diagonal algorithm and up to 5 times faster than Ellpack/Itpack method. Our preprocessing time is an order of magnitude faster than for the Jagged Diagonal algorithm. Also, using an assembly language implementation of SEGMV on a 16 processor C90, the NAS Conjugate Gradient benchmark runs at 3.5 gigaflops.