Quadratic Time Algorithms Appear to be Optimal for Sorting Evolving Data

TL;DR

This paper empirically demonstrates that quadratic-time sorting algorithms like insertion sort and bubble sort are asymptotically optimal for evolving data models with random adjacent swaps, outperforming or matching faster algorithms.

Contribution

It provides empirical evidence that quadratic algorithms are optimal in the evolving data model, filling a gap in theoretical understanding.

Findings

Quadratic algorithms perform optimally in the evolving data model.

Insertion sort and bubble sort are as effective as or better than quicksort.

Empirical results support the optimality of quadratic time algorithms for this setting.

Abstract

We empirically study sorting in the evolving data model. In this model, a sorting algorithm maintains an approximation to the sorted order of a list of data items while simultaneously, with each comparison made by the algorithm, an adversary randomly swaps the order of adjacent items in the true sorted order. Previous work studies only two versions of quicksort, and has a gap between the lower bound of Omega(n) and the best upper bound of O(n log log n). The experiments we perform in this paper provide empirical evidence that some quadratic-time algorithms such as insertion sort and bubble sort are asymptotically optimal for any constant rate of random swaps. In fact, these algorithms perform as well as or better than algorithms such as quicksort that are more efficient in the traditional algorithm analysis model.