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Optimal Guard Placement Problem Under L-Visibility

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Computational Science and Its Applications - ICCSA 2006 (ICCSA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3980))

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Abstract

Two points a and b in the presence of polygonal obstacles are L-visible if the length of the shortest path avoiding obstacles is no more than L. For a given convex polygon Q, Gewali et al [4]. addressed the guard placement problem on the exterior boundary that will cover the maximum area exterior to the polygon under L-visibility. They proposed a linear time algorithm for some given value of L. When the length L is greater than half of the perimeter, they declared that problem as open. Here we address that open problem and present an algorithm whose time complexity is linear in number of vertices of the polygon.

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References

  1. Aronov, B., Davis, A.R., Dey, T.K., Pal, S.P., Prasad, D.C.: Visibility with reflection. In: Proc. of the 11th ACM symposium on computational geometry, pp. 316–325 (1995)

    Google Scholar 

  2. Chvatal, V.: A combinatorial theorem in plane geometry. Journal of combinatorial Theory SER B 18, 39–41 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  3. ElGindy, H., Avis, D.: A linear time algorithm for computing the visibility polygon from a point. Journal of Algorithms 2, 186–197 (1981)

    Article  MathSciNet  Google Scholar 

  4. Gewali, L., Venkatasubramanian, R., Glasser, D.: Algorithms for Computing Grazing Area (unpublished results), http://www.egr.unlv.edu/~laxmi/

  5. Ntafos, S.: Watchman routes under limited visibility. Computational Geometry: Theory and Application 1, 149–170 (1992)

    MATH  MathSciNet  Google Scholar 

  6. O’Rourke, J.: Art Gallery Theorems and Algorithms. Oxford University Press, Oxford (1987)

    MATH  Google Scholar 

  7. Sack, J.R., Urrutia, J.: Handbook of computational geometry. North-Holland/Elsevier Science B. V, Netherlands (2000)

    MATH  Google Scholar 

  8. Shermer, T.: Recent results in Art Galleries. Proceedings of the IEEE, 1384–1399 (1992)

    Google Scholar 

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Author information

Authors and Affiliations

  1. LSI Logic India Pvt. Ltd., Kolkata, 700 091, India

    Debabrata Bardhan

  2. Indian Statistical Institute, Kolkata, 700 108, India

    Sasanka Roy

  3. Institut de Mathematiques, Universite de Bourgogne, Dijon, 21078, France

    Sandip Das

Authors
  1. Debabrata Bardhan
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  2. Sasanka Roy
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  3. Sandip Das
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina Gavrilova

  2. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

  3. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota, USA

    Vipin Kumar

  4. OptimaNumerics Ltd., Cathedral House, 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

  5. Clayton School of IT, Monash University, 3800, Clayton, Australia

    David Taniar

  6. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, I-06123, Perugia, Italy

    Antonio Laganá

  7. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  8. School of Information and Communication Engineering, Sungkyunkwan University, Korea

    Hyunseung Choo

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© 2006 Springer-Verlag Berlin Heidelberg

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Bardhan, D., Roy, S., Das, S. (2006). Optimal Guard Placement Problem Under L-Visibility. In: Gavrilova, M., et al. Computational Science and Its Applications - ICCSA 2006. ICCSA 2006. Lecture Notes in Computer Science, vol 3980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11751540_2

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  • DOI: https://doi.org/10.1007/11751540_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34070-6

  • Online ISBN: 978-3-540-34071-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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