Modeling and improving locality for irregular problems: Sparse matrix-Vector product on cache memories as a case study

Abstract

In this paper we introduce a model for representing and improving the locality of sparse matrices for irregular problems. We focus our attention on the behavior of iterative methods for the solution of sparse linear systems with irregular patterns. In particular the product of a sparse matrix by a dense vector (SpM×V) is closely examined, as this is one of the basic kernels in such codes. As a representative level of the memory hierarchy, we consider the cache memory. In our model, locality is measured taking into account pairs of rows or columns of sparse matrices. In order to evaluate this locality four functions based on two parameters called entry matches and cache line matches are introduced. Using an analogy of this problem to the Traveling Salesman Problem we have applied two algorithms in order to solve it; one based on the construction of minimum spanning trees and the other on the nearest-neighbor heuristic. These techniques were tested over a set of sparse matrices. The results were assesed through the measurement of cache misse on a standard cache memory.