# Load-Balancing for Parallel Delaunay Triangulations

## TL;DR

This paper introduces a data-sensitive divide-and-conquer method for parallel Delaunay triangulation that achieves balanced partitions and reduces merging time, significantly improving performance on structured datasets.

## Contribution

It proposes a novel triangulation-based partitioning approach that enhances load balancing and merging efficiency in parallel Delaunay triangulation algorithms.

## Key findings

- Nearly perfectly balanced partitions achieved.
- Small border triangulations for faster merging.
- Almost halves running time on structured datasets.

## Abstract

Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two partial triangulations by re-triangulating a small subset of their vertices - the border vertices - and combining the three triangulations efficiently via parallel hash table lookups. The input point division should therefore yield roughly equal-sized partitions for good load-balancing and also result in a small number of border vertices for fast merging. In this paper, we present a novel divide-step based on partitioning the triangulation of a small sample of the input points. In experiments on synthetic and real-world data sets, we achieve nearly perfectly balanced partitions and small border triangulations. This almost cuts running time in half compared to non-data-sensitive division schemes on inputs exhibiting an exploitable underlying structure.