On Memory Footprints of Partitioned Sparse Matrices

Abstract: Runtime characteristics of sparse matrix computations and related processes may be often improved by reducing memory footprints of involved matrices. Such a reduction can be usually achieved when matrices are processed in a block-wise manner. The presented study analysed memory footprints of 563 representative benchmark sparse matrices with respect to their partitioning into uniformly-sized blocks. Different block sizes and different ways of storing blocks in memory were considered and statistically evaluated. Memory footprints of partitioned matrices were additionally compared with lower bounds and with the CSR storage format. The average measured memory savings against CSR in case of single and double precision were 42.3 and 28.7 percents, the corresponding worst-case savings 25.5 and 17.1 percents. Moreover, memory footprints of partitioned matrices were in average 5 times closer to their lower bounds than CSR. Based on the obtained results, generic suggestions for efficient partitioning and storage of sparse matrices in a computer memory are provided.