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Finding a closest visible vertex pair between two polygons

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Abstract

Given nonintersecting simple polygonsP andQ, two verticespεP andqε Q are said to be visible if\(\overline {pq}\) does not properly intersectP orQ. We present a parallel algorithm for finding a closest pair among all visible pairs (p,q),pεP andqεQ. The algorithm runs in time O(logn) using O(n) processors on a CREW PRAM, wheren=¦P¦+¦Q¦. This algorithm can be implemented serially in Θ(n) time, which gives a new optimal sequential solution for this problem.

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Authors and Affiliations

  1. Department of Computer Science, Texas A&M University, 77843-3112, College Station, TX, USA

    N. M. Amato

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  1. N. M. Amato
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Additional information

Communicated by B. Chazelle.

This paper appeared in preliminary form as [1]. This work was supported in part by an AT&T Bell

Laboratories Graduate Fellowship, the Joint Services Electronics Program (U.S. Army, U.S. Navy, U.S. Air Force) under Contract N00014-90-J-1270, and NSF Grant CCR-89-22008. This work was done while the author was with the Department of Computer Science at the University of Illinois at Urbana-Champaign.

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Amato, N.M. Finding a closest visible vertex pair between two polygons. Algorithmica 14, 183–201 (1995). https://doi.org/10.1007/BF01293668

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  • DOI: https://doi.org/10.1007/BF01293668

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