Efficient transposition algorithms for large matrices

• Published in: Proceedings of the 1993 ACM/IEEE conference on Supercomputing pp. 656 - 665
• Main Authors: Kaushik, S. D., Huang, C.-H., Johnson, R. W., Sadayappan, P., Johnson, J. R.
• Format: Conference Proceeding
• Language: English
• Published: New York, NY, USA ACM 01.12.1993; IEEE
• Series: ACM Conferences
• Subjects: Cloud computing; Computer systems organization > Architectures > Distributed architectures > Grid computing; Computer systems organization > Architectures > Parallel architectures > Multicore architectures; Computer systems organization > Architectures > Serial architectures > Superscalar architectures; Computerized monitoring; Computing methodologies > Modeling and simulation > Simulation types and techniques > Massively parallel and high-performance simulations; Computing methodologies > Parallel computing methodologies > Parallel algorithms; Fourier transforms; Mathematics of computing > Mathematical analysis > Numerical analysis > Computation of transforms; Mathematics of computing > Mathematical analysis > Numerical analysis > Computations on matrices; NIST; Parallel algorithms; Software and its engineering > Software organization and properties > Software system structures > Distributed systems organizing principles > Grid computing; Tensile stress; Theory of computation > Design and analysis of algorithms > Parallel algorithms; Vectors
• ISBN: 0818643404; 9780818643408
• ISSN: 1063-9535
• DOI: 10.1145/169627.169814

The authors present transposition algorithms for matrices that do not fit in main memory. Transposition is interpreted as a permutation of the vector obtained by mapping a matrix to linear memory. Algorithms are derived from factorizations of this permutation, using a class of permutations related to the tensor product. Using this formulation of transposition, the authors first obtain several known algorithms and then they derive a new algorithm which reduces the number of disk accesses required. The new algorithm was compared to existing algorithms using an implementation on the Intel iPSC/860. This comparison shows the benefits of the new algorithm.