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Workshop on Algorithms and Data Structures

WADS 1993: Algorithms and Data Structures pp 48–59Cite as

An optimal algorithm for finding the separation of simple polygons

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 709))

Abstract

Given simple polygons P and Q, their separation, denoted by σ(P,Q), is defined to be the minimum distance between their boundaries. We present an optimal Θ(N) algorithm for determining the separation of two simple polygons P and Q, where ¦P¦+¦Q¦=¦N¦. The best previous algorithm for this problem is due to Kirkpatrick and has complexity O(N log N). In addition, a parallel version of our algorithm can be implemented in O(log N) time using O(N) processors on a CREW PRAM. Our results are obtained by providing a unified treatment of the separation and the closest visible vertex problems for simple polygons.

This work was supported in part by 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.

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Author information

Author notes

  1. Nancy M. Amato

    Present address: Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 1308 W. Main St., 61801, Urbana, IL

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    Authors
    1. Nancy M. Amato
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    Editor information

    Frank Dehne Jörg-Rüdiger Sack Nicola Santoro Sue Whitesides

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    © 1993 Springer-Verlag Berlin Heidelberg

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    Amato, N.M. (1993). An optimal algorithm for finding the separation of simple polygons. In: Dehne, F., Sack, JR., Santoro, N., Whitesides, S. (eds) Algorithms and Data Structures. WADS 1993. Lecture Notes in Computer Science, vol 709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57155-8_235

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    • DOI: https://doi.org/10.1007/3-540-57155-8_235

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    • Publisher Name: Springer, Berlin, Heidelberg

    • Print ISBN: 978-3-540-57155-1

    • Online ISBN: 978-3-540-47918-5

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