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arXiv · 2502.05082

A Randomised Approach to Distributed Sorting

Sam Olesker-Taylor
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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.

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Sam Olesker-Taylor. 2025-02-07. A Randomised Approach to Distributed Sorting. https://arxiv.org/abs/2502.05082

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