New Parallel-Sorting Schemes

In this paper, we describe a family of parallel-sorting algorithms for a multiprocessor system. These algorithms are enumeration sortings and comprise the following phases: 1) count acquisition: the keys are subdivided into subsets and for each key we determine the number of smaller keys (count) in every subset; 2) rank determination: the rank of a key is the sum of the previously obtained counts; 3) data rearrangement: each key is placed in the position specified by its rank. The basic novelty of the algorithms is the use of parallel merging to implement count acquisition. By using Valiant´s merging scheme, we show that n keys can be sorted in parallel with n log2n processors in time C log2n + o(log2n); in addition, if memory fetch conflicts are not allowed, using a modified version of Batcher´s merging algorithm to implement phase 1), we show that n keys can be sorted with n^{1 +α}processors in time (C´/α a) log2n + o(log2n), thereby matching the performance of Hirschberg´s algoithm, which, however, is not free of fetch conflicts.