In-Place Radix Sort

Question

This is a long text. Please bear with me. Boiled down, the question is: Is there a workable in-place radix sort algorithm?

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Preliminary

Answer 1

I've never seen an in-place radix sort, and from the nature of the radix-sort I doubt that it is much faster than a out of place sort as long as the temporary array fits into memory.

Reason:

The sorting does a linear read on the input array, but all writes will be nearly random. From a certain N upwards this boils down to a cache miss per write. This cache miss is what slows down your algorithm. If it's in place or not will not change this effect.

I know that this will not answer your question directly, but if sorting is a bottleneck you may want to have a look at near sorting algorithms as a preprocessing step (the wiki-page on the soft-heap may get you started).

That could give a very nice cache locality boost. A text-book out-of-place radix sort will then perform better. The writes will still be nearly random but at least they will cluster around the same chunks of memory and as such increase the cache hit ratio.

I have no idea if it works out in practice though.

Btw: If you're dealing with DNA strings only: You can compress a char into two bits and pack your data quite a lot. This will cut down the memory requirement by factor four over a naiive representation. Addressing becomes more complex, but the ALU of your CPU has lots of time to spend during all the cache-misses anyway.