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Optimal parallel algorithms for point-set and polygon problems

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Abstract

In this paper we give parallel algorithms for a number of problems defined on point sets and polygons. All our algorithms have optimalT(n) * P(n) products, whereT(n) is the time complexity andP(n) is the number of processors used, and are for the EREW PRAM or CREW PRAM models. 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 than point-set problems, and that nearest-neighbor problems can be solved without explicitly constructing a Voronoi diagram.

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Authors and Affiliations

  1. Courant Institute, New York University, 10012, New York, NY, USA

    Richard Cole

  2. Department of Computer Science, The Johns Hopkins University, 21218, Baltimore, MD, USA

    Michael T. Goodrich

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  1. Richard Cole
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  2. Michael T. Goodrich
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Additional information

Communicated by Alok Aggarwal.

The research of R. Cole was supported in part by NSF Grants CCR-8702271, CCR-8902221, and CCR-8906949, by ONR Grant N00014-85-K-0046, and by a John Simon Guggenheim Memorial Foundation fellowship. M. T. Goodrich's research was supported by the National Science Foundation under Grant CCR-8810568 and by the National Science Foundation and DARPA under Grant CCR-8908092.

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Cole, R., Goodrich, M.T. Optimal parallel algorithms for point-set and polygon problems. Algorithmica 7, 3–23 (1992). https://doi.org/10.1007/BF01758749

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