A Randomised Approach to Distributed Sorting

TL;DR

This paper presents a simple, randomized distributed sorting algorithm called the harmonic sorter, which achieves efficient sorting with linear speed-up in parallel and distributed environments, emphasizing its robustness and ease of implementation.

Contribution

The paper introduces the harmonic sorter, a novel randomized sorting algorithm with provable efficiency and parallelization benefits, suitable for distributed computing.

Findings

Achieves order-$n (\log n)^2$ sorting time.

Supports linear speed-up in parallel and distributed settings.

Demonstrates robustness and low communication overhead.

Abstract

We introduce and analyse a new, extremely simple, randomised sorting algorithm: - choose a pair of indices $\{i, j\}$ according to some distribution $q$; - sort the elements in positions $i$ and $j$ of the array in ascending order. Choosing $q_{\{i,j\}} \propto 1/|j - i|$ yields an order-$n (\log n)^2$ sorting time. We call it the harmonic sorter. The sorter trivially parallelises in the asynchronous setting, yielding a linear speed-up. We also exhibit a low-communication, synchronous version with a linear speed-up. We compare and contrast this algorithm with other sorters, and discuss some of its benefits, particularly its robustness and amenability to parallelisation and distributed computing.