Parallel Delaunay triangulation


The parallelization of Delaunay triangulation algorithms has been investigated, with different solutions designed and evaluated.

The first one, which is a parallel implementation of the Divide & Conquer paradigm, was faster but showed limited scalability.
The second one operates a regular geometric partition of the dataset and subdivides the load among m independent asynchronous processors, using on each node a modified version of an incremental construction algorithm (InCoDe); this solution is algorithmically quite simple and allows sufficiently good scalability.

In order to increase the scalability of the parallel incremental construction method, a hybrid strategy has been proposed in a further paper. This solution composes a space decomposition approach with a master-slave one. The hybrid parallel algorithm allows the threshold to be raised on the number of processors over which the efficiency of the other two solutions become unacceptable.

Papers

Evaluation of parallelization strategies for an incremental Delaunay triangulator in E3
P. Cignoni, D. Laforenza, C. Montani, R. Perego, and R. Scopigno
Concurrency: Practice and Experience, 7(1):61-80, 1995

Abstract
This paper deals with the parallelization of Delaunay triangulation, a widely used space partitioning technique. Two parallel implementations of a three-dimensional incremental construction algorithm are presented. The first is based on the decomposition of the spatial domain, while the second relies on the master-slaves approach.
Both parallelization strategies are evaluated, stressing practical issues rather than theoretical complexity. We report on the exploitation of two different parallel environments: a tightly-coupled distributed memory MIMD architecture and a network of workstations cooperating under the Linda environment. Then, a third hybrid solution is proposed, specifically addressed to the exploitation of higher parallelism. It combines the other two solutions by grouping the processing nodes of the multicomputer into clusters and by exploiting parallelism at two different levels.

 

Parallel 3D Delaunay triangulation
P. Cignoni, C. Montani, R. Perego, and R. Scopigno
Computer Graphics Forum, 12(3):129-142, 1993

Abstract
The paper deals with the parallelization of Delaunay triangulation algorithms, giving more emphasis to pratical issues and implementation than to theoretical complexity. Two parallel implementations are presented. The first one is built on DeWall, an Ed triangulator based on an original interpretation of the divide & conquer paradigm. The second is based on an incremental construction algorithm. The parallelization strategies are presented and evaluated. The target parallel machine is a distributed computing environment, composed of coarse grain processing nodes. Results of first implementations are reported and compared with the performance of the serial versions running on a Unix workstation.