A note on bitonic sorting

Abstract

We give an extremely simple proof of the following lemma due to Batcher: Let n ∈ N be even and let x=( x 0,…, x n−1 ) be a sequence of elements from a totally ordered set M. Let L(x)=( min{x 0, x n 2 },…, min{x n 2−1 ,x n−1}) and let H(x) = ( max{,x 0, x n 2 },…, max{x n 2−1 , x n−1}) . If x is bitonic then L( x) and H( x) are both bitonic and a ⩽ b for all elements a in L( x) and b in H( x). Efficient implementation of Batcher's bitonic sort on parallel computers depends crucially on this lemma.