Ternary sorting

The last Le Monde puzzle made me wonder about the ternary version of the sorting algorithms, which all seem to be binary (compare x and y, then…). The problem is, given (only) a blackbox procedure that returns the relative order of three arbitrary numbers, how many steps are necessary to sort a series of n nnumbers? The heapsort entry in Wikipedia mentions a ternary sorting version, but does not get into details. Robert Sedgewick (author of a fabulous book on algorithmic I enjoyed very much when I started programming) has a talk about the optimality of quicksort where he mentions ternary sorting, but this seems to be more related with ties than with my problem… It is of course highly formal in that I do not know of a physical device that would justify moving from binary to ternary comparisons.

Tags: R, rank, Le Monde, wikipedia, heapsort, quicksort, sorting