MadVoro: Parallel Construction of Voronoi Diagrams in Distributed Memory Systems

TL;DR

MadVoro is a new parallel algorithm and open-source framework for constructing 3D Voronoi diagrams efficiently in distributed memory systems, enabling scalable applications in scientific computing.

Contribution

It introduces a distributed Voronoi construction algorithm using Delaunay triangulation, with load balancing and performance comparison to existing methods.

Findings

Efficient parallel Voronoi construction in distributed systems

Open-source C++ implementation available

Performance benchmarks show competitive speedup

Abstract

Voronoi diagrams are essential geometrical structures with numerous applications, particularly astrophysics-driven finite volume methods. While serial algorithms for constructing these entities are well-established, parallel construction remains challenging. This is especially true in distributed memory systems, where each host manages only a subset of the input points. This process requires redistributing points across hosts and accurately computing the corresponding Voronoi cells. In this paper, we introduce a new distributed construction algorithm, which is implemented in our open-source C++ 3-dimensional Voronoi construction framework. Our approach leverages Delaunay triangulation as an intermediate step, which is then transformed into a Voronoi diagram. We introduce the algorithms we implemented for the precise construction and our load-balancing approach and compare the running time with other state-of-the-art frameworks. MadVoro is a versatile tool that can be applied in various scientific domains, such as mesh decomposition, computational physics, chemistry, and machine learning.