Fast deterministic sorting on large parallel machines

Many sorting algorithms that perform well on uniformly distributed data suffer significant performance degradation on non-random data. Unfortunately many real-world applications require sorting on data that is not uniformly distributed. In this paper we consider distributions of varying entropies. We describe A-Ranksort, a new sorting algorithm for parallel machines, whose behavior on input distributions of different entropies is relatively stable. Our algorithm is based on a deterministic strategy to find approximate ranks for all keys. We implemented A-Ranksort, B-Flashsort, Radixsort, and Bitonic sort on a 2048 processor Maspar MP-1. Our experiments show that A-Ranksort out-performs all the other algorithms on a variety of input distributions, when the output is required to be balanced. We are also able to provide bounds on the average-case and worst-case complexities of our algorithm, in terms of the costs of some chosen primitive operations. The predicted performance is very close to the empirical results, thus justifying our model.