Abstract
We provide the first tight bound for covering a polygon with n vertices and h holes with vertex guards. In particular, we provide tight bounds for the number of floodlights, placed at vertices or on the boundary, sufficient to illuminate the interior or the exterior of an orthogonal polygon with holes. Our results lead directly to simple linear, and thus optimal, algorithms for computing a covering of an orthogonal polygon.
This work was partially carried out under grant CONACYT 3912-A9402 in México.
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References
J. Abello, O. Egecioglu, and Kumar K. Visibility graphs of staircase polygons and the weak Bruhat order I: From polygons to maximal chains. Discrete and Computational Geometry. in press.
I. Bjorling-Sachs and D. L. Souvaine. A tight bound for guarding polygons with holes. Report LCSR-TR-165, Lab. Comput. Sci. Res., Rutgers Univ., New Brunswick, NJ, 1991.
P. Bose, L. Guibas, A. Lubiw, M. Overmars, D. Souvaine, and J. Urrutia. The floodlight problem. Int. J. On Computational Geometry. in press.
B. Chazelle. Triangulating a simple polygon in linear time. Discrete Comput. Geom., 6:485–524, 1991.
J. Czyzowicz, E. Rivera-Campo, and J. Urrutia. Optimal floodlight illumination of stages. Proc. of the 5th CCCG, pages 393–398, Waterloo, Ontario, August 1993. Univ. of Waterloo.
V. Estivill-Castro and J. Urrutia. Optimal floodlight illumination of orthogonal art galleries. In Proc. of the Sixth CCCG, pages 81–86, Saskatoon, Canada, August 1994. University of Saskatchewan.
Györi. E., F. Hoffman, K. Kriegel, and T. Shermer. Generalized guarding and partitioning for rectilinear polygons (extended abstract). In Proc. of the Sixth CCCG, pages 302–307, Saskatoon, Canada, August 1994. U. of Saskatchewan.
F. Hoffmann. On the rectilinear art gallery problem. In Proc. of the Int. Col. on Automata, Languages, and Programming 90, pages 717–728. Springer-Verlag Lecture. Notes on Computer Science 443, 1990.
F. Hoffmann, M. Kaufmann, and K. Kriegel. The art gallery theorem for polygons with holes. In Proc. 32nd IEEE Sympos. Found. Comput. Sci., pages 39–48, 1991.
J. Kahn, M. Klawe, and D. Kleitman. Traditional galleries require fewer watchmen. SIAM J. Algebraic Discrete Methods, 4:194–206, 1980.
J. O'Rourke. Art Gallery Theorems and Algorithms. Oxford University Press, New York, 1987.
G. J. E. Rawlins. Explorations in restricted-orientation geometry. Ph.D. thesis, Univ. Waterloo, Waterloo, ON, 1987.
T. Shermer. Recent results in art galleries. Proceedings of the IEEE, 80:1384–1399, 1992.
W. Steiger and I. Streuni. Positive and negative results on the floodlight problem. In Proc. of the Sixth CCCG, pages 87–92, Saskatoon, Canada, August 1994. University of Saskatchewan.
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© 1995 Springer-Verlag Berlin Heidelberg
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Abello, J., Estivill-Castro, V., Shermer, T., Urrutia, J. (1995). Illumination with orthogonal floodlights. In: Staples, J., Eades, P., Katoh, N., Moffat, A. (eds) Algorithms and Computations. ISAAC 1995. Lecture Notes in Computer Science, vol 1004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015442
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DOI: https://doi.org/10.1007/BFb0015442
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