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.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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)
Chvatal, V.: A combinatorial theorem in plane geometry. Journal of combinatorial Theory SER B 18, 39–41 (1975)
ElGindy, H., Avis, D.: A linear time algorithm for computing the visibility polygon from a point. Journal of Algorithms 2, 186–197 (1981)
Gewali, L., Venkatasubramanian, R., Glasser, D.: Algorithms for Computing Grazing Area (unpublished results), http://www.egr.unlv.edu/~laxmi/
Ntafos, S.: Watchman routes under limited visibility. Computational Geometry: Theory and Application 1, 149–170 (1992)
O’Rourke, J.: Art Gallery Theorems and Algorithms. Oxford University Press, Oxford (1987)
Sack, J.R., Urrutia, J.: Handbook of computational geometry. North-Holland/Elsevier Science B. V, Netherlands (2000)
Shermer, T.: Recent results in Art Galleries. Proceedings of the IEEE, 1384–1399 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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)