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The sparse matrix-vector multiplication (SpMxV) is a kernel operation widelyused in iterative linear solvers. The same sparse matrix is multiplied by adense vector repeatedly in these solvers. Matrices with irregular sparsitypatterns make it difficult to utilize cache locality effectively in SpMxVcomputations. In this work, we investigate single- and multiple-SpMxVframeworks for exploiting cache locality in SpMxV computations. For thesingle-SpMxV framework, we propose two cache-size-aware top-downrow/column-reordering methods based on 1D and 2D sparse matrix partitioning byutilizing the column-net and enhancing the row-column-net hypergraph models ofsparse matrices. The multiple-SpMxV framework depends on splitting a givenmatrix into a sum of multiple nonzero-disjoint matrices so that the SpMxVoperation is performed as a sequence of multiple input- and output- dependentSpMxV operations. For an effective matrix splitting required in this framework,we propose a cache- size-aware top-down approach based on 2D sparse matrixpartitioning by utilizing the row-column-net hypergraph model. For thisframework, we also propose two methods for effective ordering of individualSpMxV operations. The primary objective in all of the three methods is tomaximize the exploitation of temporal locality. We evaluate the validity of ourmodels and methods on a wide range of sparse matrices using both cache-misssimulations and actual runs by using OSKI. Experimental results show thatproposed methods and models outperform state-of-the-art schemes.

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