An in-place sorting with <i>O</i> ( <i>n</i> log <i>n</i> ) comparisons and <i>O</i> ( <i>n</i> ) moves

Abstract

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, 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.