[tim-peters]

Ya, I'm just too old for bottomless pits anymore ;-) Patience sorting is still worth study, for its elegance, simple code, and real-world practicality in the context of solving the longest increasing subsequence problem. As a full-blown sorting algorithm, it only excels at reverse-ordered and "low diversity" inputs, but that's in return for very simple, uniform, and easily understood code.

Of course any of these could be changed to use the powersort merge strategy, if desired. It's elegant and principled. But it also exploits that timsort and powersort keep the _number_ of runx simultaneously active no more than log2(N). Needing to keep track of potentially O(N) sublists simultaneously is potentially burdensome.

In any case, I'm most interested in adaptive sorting, since partial order so very often exists in the real world (as you noted that Orson Peters noted, this is often due to "low diversity" as a consequence of sorting on one field of a complex record - but it's more than just that). Thanks to your good explanations, I'm persuaded that JesseSort isn't much more promising than patience sorting in that specific respect (yes, looks like JesseSort can handle ascending order in linear time too). So thanks again!