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On Guarding Orthogonal Polygons with Sliding Cameras

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WALCOM: Algorithms and Computation (WALCOM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10167))

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Abstract

A sliding camera inside an orthogonal polygon P is a point guard that travels back and forth along an orthogonal line segment \(\gamma \) in P. The sliding camera g can see a point p in P if the perpendicular from p onto \(\gamma \) is inside P. In this paper, we give the first constant-factor approximation algorithm for the problem of guarding P with the minimum number of sliding cameras. Next, we show that the sliding guards problem is linear-time solvable if the (suitably defined) dual graph of the polygon has bounded treewidth. On the other hand, we show that the problem is NP-hard on orthogonal polygons with holes even if only horizontal cameras are allowed. Finally, we study art gallery theorems for sliding cameras, thus, give upper and lower bounds in terms of the number of sliding cameras needed relative to the number of vertices n.

T. Biedl and T.M. Chan—Research of the authors is supported by NSERC.

F. Montecchiani—Research of the author supported in part by the MIUR project AMANDA, prot. 2012C4E3KT_001. Research was done while the author was visiting the University of Waterloo.

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Authors and Affiliations

  1. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada

    Therese Biedl, Timothy M. Chan, Stephanie Lee, Saeed Mehrabi & Hamideh Vosoughpour

  2. Department of Engineering, University of Perugia, Perugia, Italy

    Fabrizio Montecchiani

Authors
  1. Therese Biedl
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  2. Timothy M. Chan
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  3. Stephanie Lee
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  4. Saeed Mehrabi
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  5. Fabrizio Montecchiani
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  6. Hamideh Vosoughpour
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Corresponding author

Correspondence to Saeed Mehrabi .

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Editors and Affiliations

  1. Universiti Teknologi Brunei, Bandar Seri Begawan, Brunei Darussalam

    Sheung-Hung Poon

  2. Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

    Md. Saidur Rahman

  3. National Taiwan University, Taipei, Taiwan

    Hsu-Chun Yen

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Biedl, T., Chan, T.M., Lee, S., Mehrabi, S., Montecchiani, F., Vosoughpour, H. (2017). On Guarding Orthogonal Polygons with Sliding Cameras. In: Poon, SH., Rahman, M., Yen, HC. (eds) WALCOM: Algorithms and Computation. WALCOM 2017. Lecture Notes in Computer Science(), vol 10167. Springer, Cham. https://doi.org/10.1007/978-3-319-53925-6_5

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  • DOI: https://doi.org/10.1007/978-3-319-53925-6_5

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  • Online ISBN: 978-3-319-53925-6

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