An 0(n log n) sorting network

@article{Ajtai1983An0L,
  title={An 0(n log n) sorting network},
  author={Mikl{\'o}s Ajtai and John Komlos and Endre Szemer{\'e}di},
  journal={Proceedings of the fifteenth annual ACM symposium on Theory of computing},
  year={1983}
}
The purpose of this paper is to describe a sorting network of size 0(n log n) and depth 0(log n). A natural way of sorting is through consecutive halvings: determine the upper and lower halves of the set, proceed similarly within the halves, and so on. Unfortunately, while one can halve a set using only 0(n) comparisons, this cannot be done in less than log n (parallel) time, and it is known that a halving network needs (½)n log n comparisons. It is possible, however, to construct a network of… 
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