Efficient Data Distribution Schemes for EKMR-Based Sparse Arrays on Distributed Memory Multicomputers

Multi-dimensional sparse array operations can be used in the atmosphere and ocean sciences, the image processing, and etc., and have been an extensively investigated problem. Therefore, it becomes an important issue to propose efficient data distribution schemes for multi-dimensional sparse arrays. In our previous work, we have proposed two data distribution schemes Compress Followed Send (CFS) and Encoding-Decoding (ED) for sparse arrays based on the traditionalmatrixrepresentation (TMR) scheme. We have proposed another scheme, called extended Karnaugh map representation (EKMR), to represent sparse arrays. The EKMR scheme can obtain better performance than the TMR scheme for some sparse array operations. Hence, in this paper, we want to propose efficient data distribution schemes for EKMR-based sparse arrays. We extend the CFS and the ED schemes for TMR-based sparse arrays to EKMR-based sparse arrays first. Then, we compare the performance of these two schemes with that of the Send Followed Compress (SFC), which is an intuitive data distribution scheme for sparse arrays. Finally, we compare these three schemes for EKMR-based sparse arrays with those of TMR-based sparse arrays, respectively. Both the theoretical analysis and the experimental tests were conducted. From the theoretical analysis and the experimental results, we can see that the ED scheme is superior to the CFS scheme that is superior to the SFC scheme for most of testing EKMR-based sparse arrays; the performance of these three schemes for EKMR-based sparse arrays is better than that of TMR-based sparse arrays for all of testing cases, respectively.