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<p><b>Abstract</b>—Array operations are useful in a large number of important scientific codes, such as molecular dynamics, finite element methods, climate modeling, atmosphere and ocean sciences, etc. In our previous work, we have proposed a scheme <it>extended Karnaugh map representation</it> (<it>EKMR</it>) for multidimensional array representation. We have shown that sequential multidimensional array operation algorithms based on the <it>EKMR</it> scheme have better performance than those based on the <it>traditional matrix representation</it> (<it>TMR</it>) scheme. Since parallel multidimensional array operations have been an extensively investigated problem, in this paper, we present efficient data parallel algorithms for multidimensional array operations based on the <it>EKMR</it> scheme for distributed memory multicomputers. In data parallel programming paradigm, in general, we distribute array elements to processors based on various distribution schemes, do local computation in each processor, and collect computation results from each processor. Based on the row, the column, and the 2D mesh distribution schemes, we design data parallel algorithms for <it>matrix-matrix addition</it> and <it>matrix-matrix multiplication</it> array operations in both <it>TMR</it> and <it>EKMR</it> schemes for multidimensional arrays. We also design data parallel algorithms for six Fortran 90 array intrinsic functions, <it>All</it>, <it>Maxval</it>, <it>Merge</it>, <it>Pack</it>, <it>Sum</it>, and <it>Cshift</it>. We compare the time of the data distribution, the local computation, and the result collection phases of these array operations based on the <it>TMR</it> and the <it>EKMR</it> schemes. The experimental results show that algorithms based on the <it>EKMR</it> scheme outperform those based on the <it>TMR</it> scheme for all test cases.</p>
Data parallel algorithm, array operation, multidimensional array, data distribution, Karnaugh map.
Jen-Shiuh Liu, Chun-Yuan Lin, Yeh-Ching Chung, "Efficient Data Parallel Algorithms for Multidimensional Array Operations Based on the EKMR Scheme for Distributed Memory Multicomputers", IEEE Transactions on Parallel & Distributed Systems, vol. 14, no. , pp. 625-639, July 2003, doi:10.1109/TPDS.2003.1214316
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