THE INPUT OUTPUT COMPLEXITY OF SORTING AND RELATED PROBLEMS

We provide tight upper and lower bounds, up to a constant factor, for the number of inputs and outputs (I/Os) between internal memory and secondary storage required for five sorting-related problems: sorting, the fast Fourier transform (FFT), permutation networks, permuting, and matrix transposition. The bounds hold both in the worst case and in the average case, and in several situations the constant factors match. Secondary storage is modeled as a magnetic disk capable of transferring P blocks each containing B records in a single time unit; the records in each block must be input from or output to B contiguous locations on the disk. We give two optimal algorithms for the problems, which are variants of merge sorting and distribution sorting.