Generic and practical sorting algorithm faster than O(n log n)?

Question

Is there any practical algorithm for generic elements (unlike counting sort or bucket sort) that runs faster than O(n log n)?

Answer 1

For how many elements? Even though it's something like N^1.2, a Shell-Metzner sort is often faster than most others up to a few thousand elements (or so).

It also depends on what you mean by "generic" and "practical". A radix sort can beat O(n log n), and it works for a fairly wide variety of data (but definitely not everything).

If your idea of practical and generic limits the algorithm to one that directly compares elements, then no -- nothing does (or ever can) be better than O(n log n). That's been proven for quite some time.