Tree-based Space Efficient Formats for Storing the Structure of Sparse Matrices

Sparse storage formats describe a way how sparse matrices are stored in a computer memory. Extensive research has been conducted about these formats in the context of performance optimization of the sparse matrix-vector multiplication algorithms, but memory efficient formats for storing sparse matrices are still under development, since the commonly used storage formats (like COO or CSR) are not sufficient. In this paper, we propose and evaluate new storage formats for sparse matrices that minimize the space complexity of information about matrix structure. The first one is based on arithmetic coding and the second one is based on binary tree format. We compare the space complexity of common storage formats and our new formats and prove that the latter are considerably more space efficient.