On Memory Footprints of Partitioned Sparse Matrices

Abstract

Abstract-The presented study analyses 563 representative benchmark sparse matrices with respect to their partitioning into uniformly-sized blocks. The aim is to minimize memory footprints of matrices. Different block sizes and different ways of storing blocks in memory are considered and statistically evaluated. Memory footprints of partitioned matrices are additionally compared with lower bounds and the CSR storage format. The average measured memory savings against CSR in case of single and double precision are 42.3 and 28.7 percents, respectively. The corresponding worst-case savings are 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, we provide generic suggestions for efficient partitioning and storage of sparse matrices in a computer memory.

Search for the Memory Duplicities in the Java Applications Using Shallow and Deep Object Comparison

“…Unfortunately, the patterns described in this work are not discovered automatically, the authors rely mostly on the manual analysis of the data structures. Another approach to the memory optimization is based on the efficient memory partitioning [10].…”

Analysis of Memory Footprints of Sparse Matrices Partitioned Into Uniformly-Sized Blocks

“…which reduces the number of tested block sizes to K × L. The rationale behind such a choice consists, e.g., of much faster block preprocessing, full employment of bits for storing in-block row and column indices, higher utilization of caches, and possible storage of block elements in Z-Morton order [26] (for detailed explanation of these aspects, see [21]).…”

“…Optimal block size Based on the analysis presented in detail in [21], we propose the following reduced sets of block sizes:…”

“…This article is an extended version of our conference paper [21]. It recapitulates main contributions of the paper and adds new material, which mainly covers following subjects:…”

“…The way how sparse matrices are stored in a computer memory may have a significant impact on the required memory space, i.e., on the matrix memory footprints. Reduction of matrix memory footprints may positively influence related computations and executions of corresponding programs [14,23,20,21]. One way of reducing memory footprints of sparse matrices is their partitioning into blocks.…”