Analysis of Sorting Algorithms by Kolmogorov Complexity (A Survey)

TL;DR

This survey reviews recent advances in analyzing sorting algorithms using Kolmogorov complexity, highlighting its effectiveness in solving longstanding open problems especially in Shellsort.

Contribution

It compiles and discusses recent results applying Kolmogorov complexity to various sorting algorithms, demonstrating its power in average-case analysis.

Findings

Kolmogorov complexity simplifies analysis of sorting algorithms.

Shellsort analysis was notably advanced using this method.

Open problems in sorting analysis were resolved.

Abstract

Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method). Especially, the usually hard average-case analysis is ammenable to this method. Here we survey such results about Bubblesort, Heapsort, Shellsort, Dobosiewicz-sort, Shakersort, and sorting with stacks and queues in sequential or parallel mode. Especially in the case of Shellsort the uses of Kolmogorov complexity surprisingly easily resolved problems that had stayed open for a long time despite strenuous attacks.