Definition: Compare, and swap if necessary, pairs of elements in parallel. Subsets are sorted then merged.
Also known as Batcher sort.
Generalization (I am a kind of ...)
Note: This takes O((log n)2/2) stages (or steps) with n/2 comparators at each stage.
This sorts increasingly larger intermingled subsets, somewhat like Shell sort, and merges subsets, like merge sort.
Elements are compared and swapped in a fixed (oblivious) schedule, so this may be implemented with only conditional swaps. Here is a Batcher sort for four elements:
compareAndSwap(0, 1);where compareAndSwap(i,j) is if (a[i] < a[j]) Swap(a[i], a[j]). Notice that the first pair of operations, (0, 1) and (2, 3), can be performed in parallel, as can the second pair (0, 2) and (1, 3).
Knuth calls this Algorithm 5.2.2M [Knuth98, 3:111].
K. E. Batcher, Sorting Networks and their Applications, Proc. AFIPS Spring Joint Computer Conference, 32:307-314, 1968.
If you have suggestions, corrections, or comments, please get in touch with Paul Black.
Entry modified 16 February 2021.
HTML page formatted Tue Feb 16 09:13:24 2021.
Cite this as:
Paul E. Black, "bitonic sort", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 16 February 2021. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/bitonicSort.html