An in-place sorting with O(nlog n) comparisons and O(n) moves. - Franceschini, Gianni (Journal of the ACM)
We present the first in-place algorithm for sorting an array of size n that performs, in the worst case, at most O(nlog n) element comparisons and O(n) element transports.This solves a long-standing open problem, stated explicitly, for example, in Munro and Raman [1992], of whether there exists a sorting algorithm that matches the asymptotic lower bounds on all computational resources simultaneously.