Improving the locality of the sparse matrix-vector product on shared memory multiprocessors

Abstract

We extend a model of locality and the subsequent process of locality improvement previously developed for the case of sparse algebra codes in monoprocessors to the case of NUMA shared memory multiprocessors (SMPs). In particular the product of a sparse matrix by a dense vector (SpM/spl times/V) is studied. In the model, locality is established at run-time considering parameters that describe the structure of the sparse matrix involved in the computations. The problem of increasing the locality is formulated as a graph problem, whose solution indicates some appropriate reordering of rows and columns of the sparse matrix. The reordering algorithms were tested for a broad set of matrices. We have also performed a comparison with other reordering algorithms. The results lead to general conclusions about improving SMP performance for other sparse algebra codes.