Efficient transposition algorithms for large matrices

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.