Today I read a paper titled “An In-Place Sorting with O(n log n) Comparisons and O(n) Moves”
The abstract is:
We present the first in-place algorithm for sorting an array of size n that performs, in the worst case, at most O(n log n) element comparisons and O(n) element transports.
This solves a long-standing open problem, stated explicitly, e.g., in [J.I.
Munro and V.
Raman, Sorting with minimum data movement, J.
Algorithms, 13, 374-93, 1992], of whether there exists a sorting algorithm that matches the asymptotic lower bounds on all computational resources simultaneously.