ExpoSort: Breaking the quasi-polynomial-time barrier for reluctant sorting

TL;DR

ExpoSort is a novel sorting algorithm that dramatically exceeds previous slow sorting methods with an intentionally inefficient $ heta(2^n)$ runtime, highlighting the delicate balance between theoretical worst-case complexity and practical performance.

Contribution

It introduces ExpoSort, the first reluctant algorithm to surpass quasi-polynomial time bounds, and demonstrates how minor code modifications can drastically alter its efficiency and nature.

Findings

ExpoSort sorts in $ heta(2^n)$ time, surpassing previous slow algorithms.

A small change converts ExpoSort into a practical insertion sort variant.

ExpoSort exemplifies the fine line between theoretical and practical algorithm design.

Abstract

We introduce the algorithm ExpoSort, a groundbreaking method that sorts an array of $n$ numbers in a spectacularly inefficient $\Theta(2^n)$ time. ExpoSort proudly claims the title of the first reluctant algorithm to decisively surpass the quasi-polynomial running time $\Omega(n^{\log n/(2+\varepsilon)})$ of the notoriously sluggish SlowSort algorithm by Broder and Stolfi [ACM SIGACT News, 1984]. In the ongoing quest for the slowest possible sort, ExpoSort redefines what it means to take one's time. Remarkably, ExpoSort achieves this feat with one of the simplest pseudocodes among all known sorting algorithms. However, a slight modification -- merely moving one recursive call inside an if statement -- transforms ExpoSort into an astonishingly well-camouflaged variant of the classic InsertionSort with best- and worst-case running times of $\Theta(n)$ and $\Theta(n^3)$, respectively. This dual nature of ExpoSort serves as a reminder of the utmost care required when crafting pessimal algorithms, where a slight lapse in judgment could result in accidentally producing an embarrassingly practical algorithm.