An O(n log n) Sorting Network

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 0(n) comparisons which halves in constant time with high accuracy. This procedure (ε-halving) and a derived procedure (ε-nearsort) are described below, and our sorting network will be centered around these elementary steps.

Authors

• Miklós Ajtai
• János Komlós
• Endre Szemerédi

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