Optimal and Sublogarithmic Time Randomized Parallel Sorting Algorithms (1989)
| Venue: | SIAM Journal on Computing |
| Citations: | 60 - 12 self |
BibTeX
@ARTICLE{Rajasekaran89optimaland,
author = {Sanguthevar Rajasekaran and John H. Reif},
title = {Optimal and Sublogarithmic Time Randomized Parallel Sorting Algorithms},
journal = {SIAM Journal on Computing},
year = {1989},
volume = {18},
pages = {594--607}
}
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Abstract
.We assume a parallel RAM model which allows both concurrent reads and concurrent writes of a global memory. Our main result is an optimal randomized parallel algorithm for INTEGER SORT (i.e., for sorting n integers in the range [1; n]). Our algorithm costs only logarithmic time and is the first known that is optimal: the product of its time and processor bounds is upper bounded by a linear function of the input size. We also give a deterministic sub-logarithmic time algorithm for prefix sum. In addition we present a sub-logarithmic time algorithm for obtaining a random permutation of n elements in parallel. And finally, we present sub-logarithmic time algorithms for GENERAL SORT and INTEGER SORT. Our sublogarithmic GENERAL SORT algorithm is also optimal. Key words. Randomized algorithms, parallel sorting, parallel random access machines, random permutations, radix sort, prefix sum, optimal algorithms. AMS(MOS) subject classifications. 68Q25. 1 A preliminary version of this paper ...
