When should we use Radix sort?

Question

It seems Radix sort has a very good average case performance, i.e. O(kN): http://en.wikipedia.org/wiki/Radix_sort

Yet it seems like most people are still using

Answer 1

Unless you have a huge list or extremely small keys, log(N) is usually smaller than k, it is rarely much higher. So choosing a general-purpose sorting algorithm with O(N log N) average case performance isn't neccesarily worse than using radix sort.

Correction: As @Mehrdad pointed out in the comments, the argument above isn't sound: Either the key size is constant, then radix sort is O(N), or the key size is k, then quicksort is O(k N log N). So in theory, radix sort really has better asymptotic runtime.

In practice, the runtimes will be dominated by terms like:

• radix sort: c1 k N

• quicksort: c2 k N log(N)

where c1 >> c2, because "extracting" bits out of a longer key is usually an expensive operation involving bit shifts and logical operations (or at least unaligned memory access), while modern CPUs can compare keys with 64, 128 or even 256 bits in one operation. So for many common cases, unless N is gigantic, c1 will be larger than c2 log(N)