Technical Report on Hypergraph-Partitioning-Based Models and Methods for Exploiting Cache Locality in Sparse-Matrix Vector Multiplication

Abstract

The sparse matrix-vector multiplication (SpMxV) is a kernel operation widely used in iterative linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers. Matrices with irregular sparsity patterns make it difficult to utilize cache locality effectively in SpMxV computations. In this work, we investigate single- and multiple-SpMxV frameworks for exploiting cache locality in SpMxV computations. For the single-SpMxV framework, we propose two cache-size-aware top-down row/column-reordering methods based on 1D and 2D sparse matrix partitioning by utilizing the column-net and enhancing the row-column-net hypergraph models of sparse matrices. The multiple-SpMxV framework depends on splitting a given matrix into a sum of multiple nonzero-disjoint matrices so that the SpMxV operation is performed as a sequence of multiple input- and output- dependent SpMxV operations. For an effective matrix splitting required in this framework, we propose a cache- size-aware top-down approach based on 2D sparse matrix partitioning by utilizing the row-column-net hypergraph model. For this framework, we also propose two methods for effective ordering of individual SpMxV operations. The primary objective in all of the three methods is to maximize the exploitation of temporal locality. We evaluate the validity of our models and methods on a wide range of sparse matrices using both cache-miss simulations and actual runs by using OSKI. Experimental results show that proposed methods and models outperform state-of-the-art schemes.