A Randomised Approach to Distributed Sorting

2025-02-07

AI Summary

This paper addresses the challenge of achieving both efficiency and low communication overhead in distributed sorting under both asynchronous and synchronous settings. We propose a minimalist randomized sorting algorithm based on harmonic distribution sampling, which repeatedly selects random index pairs and performs local sorting—naturally enabling asynchronous parallelism while smoothly transitioning to a low-communication synchronous variant. To our knowledge, this is the first harmonic sorter with an expected time complexity of $O(n(log n)^2)$, offering strong robustness, asynchronous scalability, and communication efficiency. We provide rigorous theoretical analysis proving near-linear speedup in both asynchronous and synchronous distributed environments, significantly outperforming classical comparison-based distributed sorting algorithms in terms of scalability and communication cost.

Technology Category

• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Develops a randomised sorting algorithm
• Analyzes parallel and distributed performance
• Compares with other sorting methods

Innovation

• Randomised sorting algorithm
• Harmonic sorter
• Parallel and distributed computing