Evaluating non-square sparse bilinear forms on multiple vector pairs in the I/O-model

Abstract

We consider evaluating one bilinear form defined by a sparse Ny × Nx matrix A having h entries on w pairs of vectors The model of computation is the semiring I/O-model with main memory size M and block size B. For a range of low densities (small h), we determine the I/O-complexity of this task for all meaningful choices of Nx, Ny, w, M and B, as long as M ≥ B2 (tall cache assumption). To this end, we present asymptotically optimal algorithms and matching lower bounds. Moreover, we show that multiplying the matrix A with w vectors has the same worst-case I/O-complexity. © 2010 Springer-Verlag.