Sorting takes O(n log n) in the serial case. If we have O(n) processors we would hope for a linear speedup. O(log n) parallel algorithms exist but they have a very high constant. They also aren't applicable on commodity hardware which doesn't have anywhere near O(n) processors. With p processors, reasonable algorithms should take O(n/p log n/p) time.

In the serial case, quick sort has the best runtime complexity on average. A parallel quick sort algorithm is easy to implement (see here and here). However it doesn't perform well since the very first step is to partition the whole collection on a single core. I have found information on many parallel sort algorithms but so far I have not seen anything pointing to a clear winner.

I'm looking to sort lists of 1 million to 100 million elements in a JVM language running on 8 to 32 cores.