Adaptive Shivers Sort: An Alternative Sorting Algorithm

TL;DR

Adaptive Shivers Sort is a stable mergesort algorithm that efficiently exploits existing monotonic runs in data, achieving near-optimal comparison costs for partially sorted datasets.

Contribution

It introduces a simple, stable mergesort variant that leverages monotonic runs and proves its comparison cost is nearly optimal.

Findings

Efficiently exploits monotonic runs in data

Comparison cost is near-optimal with a small additive linear term

Simple to implement stable mergesort algorithm

Abstract

We present one stable mergesort algorithm, called \Adaptive Shivers Sort, that exploits the existence of monotonic runs for sorting efficiently partially sorted data. We also prove that, although this algorithm is simple to implement, its computational cost, in number of comparisons performed, is optimal up to a small additive linear term.