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Parallel geometric algorithms on a mesh-connected computer

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Abstract

We show that a number of geometric problems can be solved on a √n × √n mesh-connected computer (MCC) inO(√n) time, which is optimal to within a constant factor, since a nontrivial data movement on an MCC requires Ω(√n) time. The problems studied here include multipoint location, planar point location, trapezoidal decomposition, intersection detection, intersection of two convex polygons, Voronoi diagram, the largest empty circle, the smallest enclosing circle, etc. TheO(√n) algorithms for all of the above problems are based on the classical divide-and-conquer problem-solving strategy.

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Author notes

  1. C. S. Jeong

    Present address: Department of Computer Science, Pohang Institute of Science and Technology, P.O. Box 125, 680, Pohang, Kyungbuk, Korea

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, 60208, Evanston, IL, USA

    C. S. Jeong & D. T. Lee

Authors
  1. C. S. Jeong
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  2. D. T. Lee
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Additional information

Communicated by Bernard Chazelle.

This work was supported in part by the National Science Foundation under Grant DCR 8420814. A preliminary version was presented in the 1987 FJCC, Dallas, TX.

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Jeong, C.S., Lee, D.T. Parallel geometric algorithms on a mesh-connected computer. Algorithmica 5, 155–177 (1990). https://doi.org/10.1007/BF01840383

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  • DOI: https://doi.org/10.1007/BF01840383

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