We present parallel computational geometry algorithms that are scalable, architecture independent, easy to implement, and have, with high probability, an optimal time complexity for uniformly distributed random input data. Our methods apply to multicomputers with arbitrary interconnection network or bus system. The following problems are studied in this paper: (1) lower envelope of line segments, (2) visibility of parallelepipeds, (3) convex hull, (4) maximal elements, (5) Voronoi diagram, (6) all-nearest neighbors, (7) largest empty circle, and (8) largest empty hyperrectangle. Problems 2-8 are studied for d-dimensional space, d=O(1). We implemented and tested the lower envelope algorithm and convex hull algorithm (for d=3 and d=4) on a CM5. The results indicate that our methods are of considerable practical relevance.

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Conference Proceeedings of the 6th IEEE Symposium on Parallel and Distributed Processing
Citation
Dehne, F, Kenyon, Claire, & Fabri, Andreas. (1994). Scalable and architecture independent parallel geometric algorithms with high probability optimal time. Presented at the Proceeedings of the 6th IEEE Symposium on Parallel and Distributed Processing.