October 16th, 2012
(written by lawrence krubner, however indented passages are often quotes). You can contact lawrence at: firstname.lastname@example.org
Bubble sort has been around a long time, and people have tried to hack it into something more efficient. One attempt at this is shaker sort. In shaker sort, there are two “bubble_sweep”s that alternate. One shifts large elements right as we did above, and the other shifts small elements left (the opposite of what we did above).
Shaker sort still takes time, but is more efficient than a naive bubble sort in practice. Shaker sort is still a dog though. A selection sort implementation easily beats it, while being much simpler (and insertion sort is better still).
But, this is where the plot thickens: the reason shaker sort is so much slower than selection sort is almost entirely down to branch mispredictions. If you care to measure, shaker sort causes fewer cache misses than selection sort, and executes a small number of extra instructions — but performs much worse due to branch mispredictions. On an unpipelined machine, this bubble sort variant might actually beat selection sort.
If there’s anything to conclude here it’s that, first and foremost, bubble sort is awful! Not only is it (in naive implementations) more instruction hungry and cache unfriendly than the other quadratic-time sorting algorithms — it manages to be fantastically confusing to branch predictors, on average at least.
The relative performance of the quadratic-time sorting algorithms is important in practice. This is the reason good quicksort implementations know to switch to insertion sort (which, as it happens causes only a linear number of branch mispredictions despite executing a quadratic number of branches).
As a result, I think it’s important to understand what’s going on behind the simple looking code of the quadratic-time sorting algorithms. It also shows that even simple and very similar looking pieces of code can behave quite differently.
And lastly, all this messing with bubble sort reminds us of Don Knuth’s near omniscience. In Volume 3 of The Art of Computer Programming, he remarks:
In short, the bubble sort seems to have nothing to recommend it, except
a catchy name and the fact that it leads to some interesting theoretical
Knuth isn’t referring to instruction pipelines when he makes this comment, but somehow he’s right about how bubble sort gets on with them too!