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Workshop on Algorithms and Data Structures

WADS 2001: Algorithms and Data Structures pp 438–449Cite as

Optimal Algorithms for Two-Guard Walkability of Simple Polygons

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2125))

Abstract

A polygon P admits a walk from a boundary point s to another boundary point t if two guards can simultaneously walk along the two boundary chains of P from s to t such that they are always visible to each other. A walk is called a straight walk if no backtracking is required during the walk. A straight walk is discrete if only one guard is allowed to move at a time, while the other guard waits at a vertex. We present simple, optimal O(n) time algorithms to determine all pairs of points of P which admit walks, straight walks and discrete straight walks. The chief merits of the algorithms are that these require simple data structures and do not assume a triangulation of P. Furthermore, the previous algorithms for the straight walk and the discrete straight walk versions ran in O(n log n) time even after assuming a triangulation.

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Author information

Authors and Affiliations

  1. School of Comput. Science, Simon Fraser Univ., Burnaby, B.C., Canada, V5A 1S6

    Binay Bhattacharya

  2. Department of Computer Science, University of Windsor, ON, Canada, N9B 3P4

    Asish Mukhopadhyay

  3. Math. Sciences Deptartment, University of Memphis, Memphis, TN, 38152, USA

    Giri Narasimhan

Authors
  1. Binay Bhattacharya
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  2. Asish Mukhopadhyay
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  3. Giri Narasimhan
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Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Candada, K1S 5B6

    Frank Dehne  & Jörg-Rüdiger Sack  & 

  2. Center for Geometric Computing, Brown University, Providence, RI, 02912-1910, USA

    Roberto Tamassia

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© 2001 Springer-Verlag Berlin Heidelberg

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Bhattacharya, B., Mukhopadhyay, A., Narasimhan, G. (2001). Optimal Algorithms for Two-Guard Walkability of Simple Polygons. In: Dehne, F., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 2001. Lecture Notes in Computer Science, vol 2125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44634-6_40

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  • DOI: https://doi.org/10.1007/3-540-44634-6_40

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42423-9

  • Online ISBN: 978-3-540-44634-7

  • eBook Packages: Springer Book Archive

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