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Starting from the left, a sorting network does a sequence of comparisons, interchanging elements if they are out of order. The network is set up so that by the time the data reaches the right-hand end, all the elements are sorted. Notice that better sorting networks tend to look more complex.
Contributed by: Stephen Wolfram (March 2011)
Open content licensed under CC BY-NC-SA
Not all types of sorting networks exist for every number of elements. Optimal networks are not yet known for more than 16 elements.
For less than 9 elements, there are no unique optimal sorting networks. Here the Batcher method achieves the minimal number of comparators for each case.