Optimal parallel algorithms for polygon and point-set problems

Authors:
R. Cole;M. T. Goodrich
Affiliations:
Courant Institute, New York Univ., New York, NY;Dept. of Computer Science, The Johns Hopkins University, Baltimore, MD
Venue:
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Year:
1988

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Abstract

In this paper we give parallel algorithms for a number of problems defined on polygons and point sets. All of our algorithms have optimal T(n) * P(n) products, where T(n) is the time complexity and P(n) is the number of processors used, and are for the EREW PRAM or CREW PRAM models. In addition, our algorithms provide parallel analogues to well known phenomena from sequential computational geometry, such as the fact that problems for polygons can oftentimes be solved more efficiently that point-set problems, and that one can solve nearest-neighbor problems without explicitly constructing a Voronoi diagram.