Efficient parallel evaluation of block properties of sparse matrices

Many storage formats for sparse matrices have been developed. Majority of these formats can be parametrized, so the algorithm for finding optimal parameters is crucial. For overall efficiency, it is important to reduce the execution time of this preprocessing. In this paper, we propose a new algorithm for the determination of the number of nonzero blocks of the given size in a sparse matrix. The proposed algorithm requires relatively a small amount of auxiliary memory. Our approach is based on the Morton reordering and bitwise manipulations. We also present a parallel (multithreaded) version and evaluate its performance and space complexity.