Plane-Sweep Incremental Algorithm: Computing Delaunay Tessellations of Large Datasets

TL;DR

This paper introduces a hybrid plane-sweep incremental algorithm for efficiently computing Delaunay tessellations of large datasets that exceed main memory, demonstrated on a dataset of 287 million points.

Contribution

The paper presents a novel hybrid approach combining incremental and plane-sweep methods to handle large-scale Delaunay tessellations efficiently.

Findings

Successfully computed tessellations for 287 million points

Memory usage limited by data set thickness along principal component

Algorithm outperforms traditional methods on large datasets

Abstract

We present the plane-sweep incremental algorithm, a hybrid approach for computing Delaunay tessellations of large point sets whose size exceeds the computer's main memory. This approach unites the simplicity of the incremental algorithms with the comparatively low memory requirements of plane-sweep approaches. The procedure is to first sort the point set along the first principal component and then to sequentially insert the points into the tessellation, essentially simulating a sweeping plane. The part of the tessellation that has been passed by the sweeping plane can be evicted from memory and written to disk, limiting the memory requirement of the program to the "thickness" of the data set along its first principal component. We implemented the algorithm and used it to compute the Delaunay tessellation and Voronoi partition of the Sloan Digital Sky Survey magnitude space consisting of 287 million points.