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What can be parallelized in computational geometry?

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Parallel Algorithms and Architectures

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 269))

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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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, 251, Mercer Street, 10012, New York, NY

    Chee-Keng Yap

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  1. Chee-Keng Yap
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Andreas Albrecht Hermann Jung Kurt Mehlhorn

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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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18099-9

  • Online ISBN: 978-3-540-47760-0

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