Optimal sparse matrix dense vector multiplication in the I/O-model

Abstract

We analyze the problem of sparse-matrix dense-vector multiplication (SpMV) in the I/O model. In the SpMV, the objective is to compute y = Ax, where A is a sparse matrix and x and y are vectors. We give tight upper and lower bounds on the number of block transfers as a function of the sparsity k, the number of nonzeros in a column of A. Parameter k is a knob that bridges the problems of permuting (k = 1) and dense matrix multiplication (k = N). When the nonzero elements of A are stored in column-major order, SpMV takes O mi