Evaluation of parallelization strategies for an incremental delaunay triangulator in E3

This paper deals with the parallelization of Delaunay triangulation, a widely used space partitioning technique which allows space to be divided into topologically elementary cells with a highly regular shape. 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 presented and valuated, 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. The results of these different implementations are evaluated and compared. 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. Keywords: Computational Geometry, Delaunay Triangulation, Parallel Processing, Distributed Computing, Linda.