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Experimental Study on Approximation Algorithms for Guarding Sets of Line Segments

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Advances in Visual Computing (ISVC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6453))

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Abstract

Consider any real structure that can be modeled by a set of straight line segments. This can be a network of streets in a city, tunnels in a mine, corridors in a building, pipes in a factory, etc. We want to approximate a minimal number of locations where to place “guards” (either men or machines), in a way that any point of the network can be “seen” by at least one guard. A guard can see all points on segments it is on (and nothing more). As the problem is known to be NP-hard, we consider three greedy-type algorithms for finding approximate solutions. We show that for each of these, theoretically the ratio of the approximate to the optimal solution can increase without bound with the increase of the number of segments. Nevertheless, our extensive experiments show that on randomly generated instances, the approximate solutions are always very close to the optimal ones and often are, in fact, optimal.

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Author information

Authors and Affiliations

  1. Mathematics Department, SUNY Buffalo State College, Buffalo, NY, 14222, USA

    Valentin E. Brimkov

  2. Mathematics Department, University at Buffalo, Buffalo, NY, 1426-2900, USA

    Andrew Leach, Michael Mastroianni & Jimmy Wu

Authors
  1. Valentin E. Brimkov
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  2. Andrew Leach
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  3. Michael Mastroianni
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  4. Jimmy Wu
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Nevada, 89557, Reno, NV, USA

    George Bebis

  2. NASA Ames Research Center, 94035, Moffett Field, CA, USA

    Richard Boyle

  3. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Bahram Parvin

  4. Desert Research Institute, Reno, NV, USA

    Darko Koracin

  5. The Chinese University of Hong Kong, Shatin, Hong Kong, China

    Ronald Chung

  6. Dyna Vox Systems, Pittsburgh, PA, USA

    Riad Hammoud

  7. King Saud University, Riyadh, Saudi Arabia

    Muhammad Hussain

  8. Hewlett Packard Labs, Paolo Alto, CA, USA

    Tan Kar-Han

  9. The Ohio State University, Columbus, OH, USA

    Roger Crawfis

  10. Virtual Reality Lab, EPFL, Lausanne, Switzerland

    Daniel Thalmann

  11. NASA Ames Research Center, Clifton Park, NY, USA

    David Kao

  12. Kitware, Clifton Park, NY, USA

    Lisa Avila

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Brimkov, V.E., Leach, A., Mastroianni, M., Wu, J. (2010). Experimental Study on Approximation Algorithms for Guarding Sets of Line Segments. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2010. Lecture Notes in Computer Science, vol 6453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17289-2_57

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  • DOI: https://doi.org/10.1007/978-3-642-17289-2_57

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17288-5

  • Online ISBN: 978-3-642-17289-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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