A parallel algorithm for Delaunay triangulation of moving points on the plane

TL;DR

This paper introduces a parallel algorithm for updating Delaunay triangulations of moving points, significantly improving efficiency over sequential methods, especially for large datasets with slow-moving points.

Contribution

The paper presents a novel parallel algorithm that divides datasets into partitions, updating Delaunay triangulations efficiently for moving points, outperforming traditional serial algorithms.

Findings

Parallel algorithm is faster than serial algorithms.

Effective for large datasets with slow-moving points.

Partitioning approach maintains Delaunay constraints after each update.

Abstract

Delaunay Triangulation(DT) is one of the important geometric problems that is used in various branches of knowledge such as computer vision, terrain modeling, spatial clustering and networking. Kinetic data structures have become very important in computational geometry for dealing with moving objects. However, when dealing with moving points, maintaining a dynamically changing Delaunay triangulation can be challenging. So, In this case, we have to update triangulation repeatedly. If points move so far, it is better to rebuild the triangulation. One approach to handle moving points is to use an incremental algorithm. For the case that points move slowly, we can give a faster algorithm than rebuilding it. Furthermore, sequential algorithms can be computationally expensive for large datasets. So, one way to compute as fast as possible is parallelism. In this paper, we propose a parallel algorithm for moving points. we propose an algorithm that divides datasets into equal partitions and give every partition to one block. Each block satisfay the Delaunay constraints after each time step and uses delete and insert algorithms to do this. We show this algorithm works faster than serial algorithms.