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An Efficient Algorithm for Out-of-Core Matrix Transposition
April 2002 (vol. 51 no. 4)
pp. 420-438

Efficient transposition of Out-of-core matrices has been widely studied. These efforts have focused on reducing the number of I/O operations. However, in state-of-the-art architectures, memory-memory data transfer time and index computation time are also significant components of the overall time. In this paper, we propose an algorithm that considers the index computation time and the I/O time and reduces the overall execution time. Our algorithm reduces the total execution time by reducing the number of I/O operations and eliminating the index computation. In doing so, two techniques are employed: writing the data onto disk in predefined patterns and balancing the number of disk read and write operations. The index computation time, which is an expensive operation involving two divisions and a multiplication, is eliminated by partitioning the memory into read and write buffers. The expensive in-processor permutation is replaced by data collection from the read buffer to the write buffer. Even though this partitioning may increase the number of I/O operations for some cases, it results in an overall reduction in the execution time due to the elimination of the expensive index computation. Our algorithm is analyzed using the well-known Linear Model and the Parallel Disk Model. The experimental results on Sun Enterprise, SGI R12000, and Pentium III show that our algorithm reduces the overall execution time by up to 50 percent compared with the best known algorithms in the literature.

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Index Terms:
matrix transpose, data transfer time, index computation time, I/O time, out-of-core, execution time
J. Suh, V.K. Prasanna, "An Efficient Algorithm for Out-of-Core Matrix Transposition," IEEE Transactions on Computers, vol. 51, no. 4, pp. 420-438, April 2002, doi:10.1109/12.995452
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