Simple and Fast BlockQuicksort using Lomuto's Partitioning Scheme

TL;DR

This paper introduces simplified variants of BlockQuicksort using Lomuto's partitioning, including a novel two-pivot approach, demonstrating comparable practical performance despite higher theoretical costs.

Contribution

The paper proposes new simplified BlockQuicksort variants with Lomuto's partitioning and a novel two-pivot scheme, enhancing robustness and ease of implementation.

Findings

Lomuto-based approaches have higher average sorting costs than Hoare-based methods.

The new variants perform comparably to original BlockQuicksort in experiments.

The analysis guides effective pivot selection for two-pivot schemes.

Abstract

This paper presents simple variants of the BlockQuicksort algorithm described by Edelkamp and Weiss (ESA 2016). The simplification is achieved by using Lomuto's partitioning scheme instead of Hoare's crossing pointer technique to partition the input. To achieve a robust sorting algorithm that works well on many different input types, the paper introduces a novel two-pivot variant of Lomuto's partitioning scheme. A surprisingly simple twist to the generic two-pivot quicksort approach makes the algorithm robust. The paper provides an analysis of the theoretical properties of the proposed algorithms and compares them to their competitors. The analysis shows that Lomuto-based approaches incur a higher average sorting cost than the Hoare-based approach of BlockQuicksort. Moreover, the analysis is particularly useful to reason about pivot choices that suit the two-pivot approach. An extensive experimental study shows that, despite their worse theoretical behavior, the simpler variants perform as well as the original version of BlockQuicksort.