Engineering In-place (Shared-memory) Sorting Algorithms

TL;DR

This paper introduces highly efficient in-place sorting algorithms, notably IPS$^4$o, that outperform existing methods across various data types, distributions, and hardware configurations by combining cache-efficient, parallel, and adaptive techniques.

Contribution

The paper presents a novel blockwise in-place data distribution technique and a robust, highly optimized comparison-based sorting algorithm, IPS$^4$o, that significantly outperforms prior in-place and non-in-place algorithms.

Findings

IPS$^4$o outperforms the best in-place parallel comparison sorts by nearly three times.

The new in-place radix sorter is optimal for many scenarios involving small keys or near-uniform distributions.

Extensive experiments confirm the robustness and superiority of the proposed algorithms across diverse settings.

Abstract

We present sorting algorithms that represent the fastest known techniques for a wide range of input sizes, input distributions, data types, and machines. A part of the speed advantage is due to the feature to work in-place. Previously, the in-place feature often implied performance penalties. Our main algorithmic contribution is a blockwise approach to in-place data distribution that is provably cache-efficient. We also parallelize this approach taking dynamic load balancing and memory locality into account. Our comparison-based algorithm, In-place Superscalar Samplesort (IPS$^4$o), combines this technique with branchless decision trees. By taking cases with many equal elements into account and by adapting the distribution degree dynamically, we obtain a highly robust algorithm that outperforms the best in-place parallel comparison-based competitor by almost a factor of three. IPS$^4$o also outperforms the best comparison-based competitors in the in-place or not in-place, parallel or sequential settings. IPS$^4$o even outperforms the best integer sorting algorithms in a wide range of situations. In many of the remaining cases (often involving near-uniform input distributions, small keys, or a sequential setting), our new in-place radix sorter turns out to be the best algorithm. Claims to have the, in some sense, "best" sorting algorithm can be found in many papers which cannot all be true. Therefore, we base our conclusions on extensive experiments involving a large part of the cross product of 21 state-of-the-art sorting codes, 6 data types, 10 input distributions, 4 machines, 4 memory allocation strategies, and input sizes varying over 7 orders of magnitude. This confirms the robust performance of our algorithms while revealing major performance problems in many competitors outside the concrete set of measurements reported in the associated publications.