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.
Supported by NSF Grants #DCR-84-01898 and #DCR-84-01633. This is based on an invited talk at the International Workshop on Parallel Algorithms and Architectures, Humboldt University, Berlin, DDR, May 25–30, 1987.
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© 1987 Springer-Verlag Berlin Heidelberg
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Yap, CK. (1987). What can be parallelized in computational geometry?. In: Albrecht, A., Jung, H., Mehlhorn, K. (eds) Parallel Algorithms and Architectures. Lecture Notes in Computer Science, vol 269. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18099-0_45
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DOI: https://doi.org/10.1007/3-540-18099-0_45
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