When that thread came up originally, I was intrigued by the idea of the dual-pivot quicksort, and went on to browse Robert Sedgewick's Ph.D. thesis, _Quicksort_, published in 1978. Sedgewick considers and analyzes several variants of quicksort in his thesis, and I've quickly discovered that he analyzes and dismisses the dual-pivot variant under a different name. I don't know whose analysis is better, but it does follow that we shouldn't treat dual-pivot qsort as an original invention (not to detract from Vladimir Yaroslavskiy's doubtless ingenuity).

Here's an excerpt from the email I wrote to Prof. Sedgewick back then; he didn't reply, so I've no idea what he thinks about this:

"I believe that your PhD thesis studies this under the name of "double partition modification". I could find no real difference between the two algorithms. Yaroslavsky claims to achieve a factor of 0.8 improvements over the standard quicksort on the number of exchanges (neutral on comparisons), while your analysis led you to reject the technique after concluding it required many more comparisons than the standard quicksort. I've only attempted very cursorily to reconcile the math; it seems that both your thesis and Yaroslavsky arrive at 0.8n(log n) as the average number of swaps, but you have (1/3) n(log n) as the average number of swaps in the classic algorithm while Yaroslavsky has 1.0 n(log n) for the same thing, so what he sees as an improvement you viewed as a disaster. My interpretation of this may be wrong, and I haven't attempted to verify either analysis yet."

The "classic algorithm" in the above is the classic quicksort as presented by Sedgewick in the thesis, which is slightly different than e.g. the standard Java implementation. I lost interest soon thereafter and stopped investigating this, but it shouldn't be too difficult to find out who was right in that algorithm comparison, if someone's interested enough.

The asymptotic optimality of samplesort is in the sense that it takes (1 + o(1)) N log N / log 2 comparisons, i.e., you can't beat it by any constant factor.

Bentley's comments from that email don't make any sense to me. I can't understand what he was thinking, unless he's just unusually prone to flattering other people's work (I don't know Bentley personally, but I've met other people who do this, much to my irritation).