Efficient Converting of Large Sparse Matrices to Quadtree Format

Abstract

Computations with sparse matrices are widespread in scientific projects. Used data format affects strongly the performance and also the space-efficiency. Commonly used storage formats (such as COO or CSR) are not suitable neither for some numerical algebra operations (e.g., The sparse matrix-vector multiplication) due to the required indirect addressing nor for I/O file operations with sparse matrices due to their high space complexities. In our previous papers, we prove that the idea of using the quad tree for these purposes is viable. In this paper, we present a completely new algorithm based on bottom-up approach for the converting matrices from common storage formats to the quad tree format. We derive the asymptotic complexity of our new algorithm, design the parallel variant of the classical and the new algorithm, and discuss their performance.