An Efficient Algorithm for Out-of-Core Matrix Transposition

E cient transposition of Out-of-core matrices has been widely studied. These e orts have focused on reducing the number of I/O operations. However, in the state-of-the-art architectures, memory-memory data transfer time and index computation time are also signi cant 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 prede ned 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 bu ers. The expensive in-processor permutation is replaced by data collection from the read bu er to the write bu er. 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%, compared with the best known algorithms in the literature.