An In-Place Sorting with O(n log n) Comparisons and O(n) Moves

TL;DR

This paper introduces a novel in-place sorting algorithm that achieves optimal comparison and move bounds simultaneously, solving a long-standing open problem in algorithm design.

Contribution

It presents the first in-place sorting algorithm with worst-case O(n log n) comparisons and O(n) moves, matching theoretical lower bounds.

Findings

Achieves optimal comparison complexity in-place

Minimizes data movement to linear in array size

Resolves a long-standing open problem in sorting algorithms

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, 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.