Efficient data compression methods for multi-dimensional sparse array operations

Abstract

For sparse array operations, in general, the sparse arrays are compressed by some data compression schemes in order to obtain better performance. The Compressed Row/Column Storage (CRS/CCS) schemes are the two common used data compression schemes for sparse arrays in the traditional matrix representation (TMR). When extended to higher dimensional sparse arrays, array operations using the CRS/CCS schemes usually do not perform well. We propose two data compression schemes, extended Karnaugh map representation Compressed Row/Column Storage (ECRS/ ECCS) for multi-dimensional sparse arrays based on the EKMR scheme. To evaluate the proposed schemes, both theoretical analysis and experimental tests are conducted. In theoretical analysis, we analyze CRS/CCS and ECRS/ECCS schemes in terms of the time complexity, the space complexity, and the range of their usability for practical applications. In experimental test, we compare the performance of matrix-matrix addition and matrix-matrix multiplication sparse array operations that use the CRS/CCS and ECRS/ECCS schemes. The experimental results show that sparse array operations based on the ECRS/ECCS schemes outperform those based on the CRS/CCS schemes for all test samples.