Nearly-Optimal Mergesorts: Fast, Practical Sorting Methods That Optimally Adapt to Existing Runs

TL;DR

This paper introduces two stable mergesort variants, peeksort and powersort, which efficiently exploit existing runs to achieve nearly-optimal merging orders with minimal overhead, outperforming previous methods in practicality.

Contribution

The paper presents novel stable mergesort algorithms that find nearly-optimal merging orders efficiently, with theoretical guarantees and practical competitiveness.

Findings

Methods are competitive with state-of-the-art stable sorts.

Achieve nearly-optimal merging with negligible overhead.

Provide constant-factor optimal worst-case guarantees.

Abstract

We present two stable mergesort variants, "peeksort" and "powersort", that exploit existing runs and find nearly-optimal merging orders with practically negligible overhead. Previous methods either require substantial effort for determining the merging order (Takaoka 2009; Barbay & Navarro 2013) or do not have a constant-factor optimal worst-case guarantee (Peters 2001; Auger, Nicaud & Pivoteau 2015; Buss & Knop 2018). We demonstrate that our methods are competitive in terms of running time with state-of-the-art implementations of stable sorting methods.