Implementation of Voronoi Using UPC

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Dr. Christian Trefftz, trefftzc@gvsu.edu

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The project deals with an implementation of Voronoi diagrams using Unified Parallel C. Voronoi diagram belong to classical problems of the computational geometry. Its origin dates back into 1850 when it was considered by Dirichlet. The rigid mathematical fundamental was given by Voronoi in 1908.

In many applications, Voronoi diagrams are already the final solution. For example, study of behavior and maintenance of live creature, which are depended on number of neighbors with whom they are fighting for food and lightness is exactly what Voronoi diagram expresses. However, having a Voronoi diagram, many important geometric features like searching for the closest neighbor, Delaunay triangulation, searching for the largest empty circle, minimum spanning tree (Euclidean tree), can be determined in the linear time.

Unified Parallel C (UPC) is an extension of the C programming language designed for high performance computing on large-scale parallel machines, including those with a common global address space (SMP and NUMA) and those with distributed memory (clusters).

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