NeatSort - A practical adaptive algorithm

TL;DR

NeatSort is a simple, efficient adaptive sorting algorithm that performs close to the theoretical lower bound for nearly sorted data and outperforms traditional quicksort implementations in practical scenarios.

Contribution

Introduces NeatSort, a new adaptive sorting algorithm with optimal disorder metrics performance and simple implementation, outperforming standard sorting methods in practice.

Findings

NeatSort has a theoretical lower bound of Ω(|X|) and an upper bound of O(|X| log |X|).

NeatSort performs better than qsort and quicksort on various data sets.

NeatSort adapts effectively to the level of disorder in the input data.

Abstract

We present a new adaptive sorting algorithm which is optimal for most disorder metrics and, more important, has a simple and quick implementation. On input $X$, our algorithm has a theoretical $\Omega (|X|)$ lower bound and a $\mathcal{O}(|X|\log|X|)$ upper bound, exhibiting amazing adaptive properties which makes it run closer to its lower bound as disorder (computed on different metrics) diminishes. From a practical point of view, \textit{NeatSort} has proven itself competitive with (and often better than) \textit{qsort} and any \textit{Random Quicksort} implementation, even on random arrays.