An optimal parallel algorithm for sorting presorted files

Abstract

We present a cost optimal parallel algorithm for sorting presorted files. The measure of presortedness we consider is the number of inversions in the input file. The algorithm sorts a file of length n, with O(mn) inversions, in O(log n(log* n − log* m)) time, provided $O(\frac{{n\log m}}{{\log n \cdot (\log ^* n - \log ^* m)}})$ processors are available, in the EREW PRAM model. This is the first PRAM sorting algorithm which is cost optimal, with respect to the number of inversions. Our method uses a new approach, which can also be used to derive a simple sequential sorting algorithm, which is efficient with respect to the number of inversions.