Implementation and Evaluation of an Eecient Parallel Delaunay Triangulation Algorithm

This paper describes the derivation of an empirically ee-cient parallel two-dimensional Delaunay triangulation program from a theoretically eecient CREW PRAM algorithm. Compared to previous work, the resulting implementation is not limited to datasets with a uniform distribution of points, achieves signiicantly better speedups over good serial code, and is widely portable due to its use of MPI as a communication mechanism. Results are presented for a loosely-coupled cluster of workstations, a distributed-memory multicom-puter, and a shared-memory multiprocessor. The Machi-avelli toolkit used to transform the nested data parallelism inherent in the divide-and-conquer algorithm into achievable task and data parallelism is also described and compared to previous techniques. 1 Introduction Delaunay triangulation represents an important substep in many computationally-intensive applications, including pattern recognition, terrain modelling, and mesh generation for the solution of partial diierential equations. Delaunay trian-gulations and their duals, Voronoi diagrams, are among the most widely-studied structures in computational geometry. Voronoi diagrams have also appeared in many other elds under diierent names 2]; domains of action in crystallography , Wigner-Seitz zones in metallurgy, Thiessen polygons in geography, and Blum's transforms in biology. This paper assumes that the reader is familiar with the basic deenition of Delaunay triangulation in R