Parallel Algorithms and Architectures pp 184-195 | Cite as

# What can be parallelized in computational geometry?

Invited Papers

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## Abstract

This paper has two goals. First, we point out that most problems in computational geometry in fact have fast parallel algorithms (that is, in *NC**) by reduction to the cell decomposition result of Kozen and Yap. We illustrate this using a new notion of generalized Voronoi diagrams that subsumes all known instances. While the existence of *NC** algorithms for computational geometry is theoretically significant, it leaves much to be desired for specific problems. Therefore, the second part of the paper surveys some recent results in a fast growing list of parallel algorithms for computational geometry.

## Keywords

Convex Hull Parallel Algorithm Voronoi Diagram Computational Geometry Delaunay Triangulation
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© Springer-Verlag Berlin Heidelberg 1987