Proceedings ArticleDOI
An 0(n log n) sorting network
Miklós Ajtai,János Komlós,Endre Szemerédi +2 more
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TLDR
A sorting network of size 0(n log n) and depth 0(log n) is described, and a derived procedure (&egr;-nearsort) are described below, and the sorting network will be centered around these elementary steps.Abstract:
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 (e-halving) and a derived procedure (e-nearsort) are described below, and our sorting network will be centered around these elementary steps.read more
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Periodic, random-fault-tolerant correction networks
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References
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Proceedings ArticleDOI
On non-linear lower bounds in computational complexity
TL;DR: It is shown that the graph of any algorithm for any one of a number of arithmetic problems (e.g. polynomial multiplication, discrete Fourier transforms, matrix multiplication) must have properties closely related to concentration networks.