Bitonic Sort

I wanted to write a short explanation about bitonic sort because it's simple as hell but no one does a good job at explaining it correctly.

You can find the video explanation here https://www.youtube.com/watch?v=GEQ8y26blEY but it's a bit tedious so to sum up the algorithm, here's what you need to know:

• A bitonic sequence is a sequence of numbers that can be ordered as first ascending then descending (or the opposite)
  • For example: (1, 2, 3, 4) followed by (4,3,2,1) is bitonic.

• The bitonic sort algorithm works in 2 parts:
  • (1) First, you need to transform any random sequence of numbers into a bitonic sequence
  • (2) Second, you can then sort the bitonic sequence in ascending order

And that is all there is to it! Now let's see how to execute the 2 parts of the algorithm.

Quick Algorithm

Part 1: Transforming any sequence of numbers into a bitonic sequence

It's a log2(N) algorithm where we recursively compare and swap elements 2 by 2 in a very specific manner.

For 8 values, we first perform 4 compare&swaps like this (pass 1):

Then we perform 4 compares&swaps like this (pass 2):

Finally we perform 4 compares&swaps like this (pass 3):

Part 2: Sorting the bitonic sequence

Well it's another log2(N) algorithm as in part 1. You'll need to swap numbers log2(N) times.

For 8 values, we first perform 4 compares&swaps like this (pass 1):

Then we perform 4 compares&swaps like this (pass 2):

Finally we perform 4 compares&swaps like this (pass 3):

Example

Here x0, x1, ..., xn}+ describes a set of values in ascending order and {x0, x1, ..., xn}- describes a set of values in descending order. While { {...}+, {...}- }B describes a bitonic sequence.

Initial random sequence: 35, 16, 31, 4, 4, 16, 17, 12

After part 1 pass 1: {{16, 35}+, {31, 4}-}B, {{4, 16}+, {17, 12}-}B ← We already have 2 size 4 bitonic sequences

After part 1 pass 2: 16, 4, 31, 35, 17, 16, 4, 12 ← It's becoming somewhat random again while we're sorting the 2 size 4 bitonic sequences into a single size 8 sequence

After part 1 pass 3: {{4, 16, 31, 35}+, {17, 16, 12, 4}-}B ← And we're done!