This paper describes the design and implementation of a practical parallel algorithm for Delaunay triangulation that works well on general distributions. Although there have been many theoretical parallel algorithms for the problem, and some implementations based on bucketing that work well for uniform distributions, there has been little work on implementations for general distributions. We use the well known reduction of 2D Delaunay triangulation to find the 3D convex hull of points on a paraboloid. Based on this reduction we developed a variant of the Edelsbrunner and Shi 3D convex hull algorithm, specialized for the case when the point set lies on a paraboloid. This simplification reduces the work required by the algorithm (number of operations) from O(n log 2 n) to O(n log n). The depth (parallel time) is O(log 3 n) on a CREW PRAM. The algorithm is simpler than previous O(n log n) work parallel algorithms leading to smaller constants.Initial experiments using a variety of distributions showed that our parallel algorithm was within a factor of 2 in work from the best sequential algorithm. Based on these promising results, the algorithm was implemented using C and an MPI-based toolkit. Compared with previous work, the resulting implementation achieves significantly better speedups over good sequential code, does not assume a uniform distribution of points, and is widely portable due to its use of MPI as a communication mechanism. Results are presented for the IBM SP2, Cray T3D, SGI Power Challenge, and DEC AlphaCluster.

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This paper gives an overview of the implementation of NESL, a portable nested data-parallel language. This language and its implementation are the first to fully support nested data structures as well as nested dataparallel function calls. These features allow the concise description of parallel algorithms on irregular data, such as sparse matrices and graphs. In addition, they maintain the advantages of data-parallel languages: a simple programming model and portability. The cur- rent NESL implementation is based on an intermediate language called VCODE and a library of vector routines called CVL. It runs on the ConnectionMachine CM-2, the Cray Y-MP C90, and serial machines. We compare initial benchmark results of NESL with those of machine-specific code on these machines for three algorithms:least-squares line-fitting, median finding, and a sparse-matrix vector product. These results show that NESL'S performance is competitive with that of machine-specific codes for regular dense data, and is often superior for irregular data.

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