Large-scale semi-discrete optimal transport with distributed Voronoi diagrams

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics Pub Date : 2025-09-14 DOI:10.1016/j.jcp.2025.114374

Bruno Lévy , Nicolas Ray , Quentin Mérigot , Hugo Leclerc

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引用次数: 0

Abstract

In this article, we propose a numerical method to solve semi-discrete optimal transport problems for gigantic pointsets (

10^{8}

points and more). By pushing the limits by several orders of magnitude, it opens the path to new applications in cosmology, fluid simulation and data science to name but a few. The method is based on a new algorithm that computes (generalized) Voronoi diagrams in parallel and in a distributed way. First we make the simple observation that the cells defined by a subgraph of the Delaunay graph contain the Voronoi cells, and that one can deduce the missing edges from the intersections between those cells. Based on this observation, we introduce the Distributed Voronoi Diagram algorithm (DVD) that can be used on a cluster and that exchanges vertices between the nodes as need be. We also report early experimental results, demonstrating that the DVD algorithm has the potential to solve some giga-scale semi-discrete optimal transport problems encountered in computational cosmology.

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具有分布Voronoi图的大规模半离散最优输运

本文提出了求解超大点集（108点以上）半离散最优输运问题的数值方法。通过将极限提升几个数量级，它为宇宙学、流体模拟和数据科学等领域的新应用开辟了道路。该方法基于一种新的算法，以并行和分布式的方式计算（广义）Voronoi图。首先，我们做了一个简单的观察，即由Delaunay图的子图定义的细胞包含Voronoi细胞，并且可以从这些细胞之间的交点推断出缺失的边。基于这一观察，我们引入了分布式Voronoi图算法（DVD），该算法可用于集群，并根据需要在节点之间交换顶点。我们还报告了早期的实验结果，表明DVD算法具有解决计算宇宙学中遇到的一些千兆级半离散最优传输问题的潜力。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational Physics 物理-计算机：跨学科应用

CiteScore

7.60

自引率

14.60%

发文量

763

审稿时长

5.8 months

期刊介绍： Journal of Computational Physics thoroughly treats the computational aspects of physical problems, presenting techniques for the numerical solution of mathematical equations arising in all areas of physics. The journal seeks to emphasize methods that cross disciplinary boundaries. The Journal of Computational Physics also publishes short notes of 4 pages or less (including figures, tables, and references but excluding title pages). Letters to the Editor commenting on articles already published in this Journal will also be considered. Neither notes nor letters should have an abstract.