Sorting Real Numbers in $O(n\sqrt{\log n})$ Time and Linear Space

TL;DR

This paper introduces a novel algorithm that sorts real numbers in $O(n\sqrt{\log n})$ time using linear space, surpassing the traditional comparison-based sorting lower bound.

Contribution

The paper presents the first known algorithm achieving sub-$n\log n$ time complexity for sorting real numbers, breaking the comparison sorting barrier.

Findings

Sorts real numbers in $O(n\sqrt{\log n})$ time

Uses linear space

Breaks the comparison sorting lower bound

Abstract

We present an $O(n\sqrt{\log n})$ time and linear space algorithm for sorting real numbers. This breaks the long time illusion that real numbers have to be sorted by comparison sorting and take $\Omega (n\log n)$ time to be sorted.