Feature Column

Diagonals: Part I

6. References

Aggarwal, A., The art gallery theorem: its variations, applications and algorithmic aspects, Ph.D. Thesis, Johns Hopkins University, Baltimore, 1984.

Aggarwal, A., and S. Suri, Computing the longest diagonal of a simple polygon, Inform. Process. Lett., 35 (1990) 13-18.

Bjorling-Sachs, I., Tight bound for edge guards in rectilinear monotone polygons, DIMACS Tech. Report, 93-12, Rutgers University, 1993.

Chazelle, B., Triangulating a simple polygon in linear time, Disc. Comput. Geom., 6 (1991) 485-524.

Chin, W-P. and S. Ntafos, Shortest watchman routes in simple polygons, Discrete Comut. Geom., 6 (1991) 9-31.

Chvátal, V., A combinatorial theorem in plane geometry, JCT (B), 18 (1975) 39-41.

Czyzowicz, J. and E. Rivera-Campo, J. Urrutia, J. Zaks, Illuminating and guarding segments in the plane, Discr. Math., 137 (1995) 147-153.

De Berg, M. and M. van Kreveld, M. Overmans, O. Schwarzkopf, Polygon Triangulation: Guarding an Art Gallery, Chapter 3, in Computational Geometry: Algorithms and Applications, 2nd. rev. ed., Springer-Verlag, Berlin, 2000.

Deneen, L. and G. Shute, Polygonizations of point sets in the plane, Disc. and Comp. Geo., 3 (1988) 77-87,

Estivill-Castro, V. and J. O'Rourke, J. Urrutia, D. Xu, Illumination of polygons with vertex floodlights, Inform. Process. Lett., 56 (1995) 9-13.

Fejes-Tóth, L., Illumination of convex disks, Acta Math. Acad. Sci. Hungar., 29 (1977) 355-360.

Fekete, S., On simple polygonalizations with optimal area, Discrete and
Computational Geometry, 23 (2000) 73-110.

Fisk, S., A short proof of Chvátal's watchman theorem, JCT (B) 24 (1978) 374.

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Gewali, L., Placing guards inside orthogonal polygons, Inform. Sci., 88 (1996) 1-14.

Gewali, L. and S. Ntafos, Cover grids and orthogonal polygons with periscope guards, Comput. Geom., 2 (1993) 309-334.

Ghosh, S., Approximation algorithms for art gallery problems, Proc. Canadian Inform. Process. Soc. Congress, 1987.

Goodman, J. and J. O'Rourke (eds.), Handbook of Discrete and Computational Geometry, CRC Press, Boca Raton, 1997.

Grünbaum, B., Hamiltonian polygons and polyhedra, Geombinatorics, 3 (1994) 83-89.

Gyõri, A short proof of the rectilinear art gallery theorem, SIAM J. Algebraic Discrete Methods, 7 (1986) 452-454.

Hershberger, J. and S. Suri, Finding a shortest diagonal of a simple polygon in linear time, Comput. Geom., 7 (1997) 149-160.

Hoffmann, F., On the rectilinear art gallery problem, ICALP 90 Automata, Languages and Programming, LNCS, Vol. 443, pp. 717-728, Springer, July 1990.

Honsberger, R., Mathematical Gems II, Mathematical Association of America, Washington, 1976, p. 104-110.

Kahn, J. and M. Klawe, D. Kleitman, Traditional galleries require fewer watchmen, SIAM J. Alg. Disc. Math., 4 (1993) 194-206.

Kalai, G. and J. Matousek, Guarding galleries where every point sees a large area, Israel J. Math., 101 (1997) 125-139.

Lee, D. and A. Lin, Computational Complexity of Art Gallery Problems, IEEE Transactions on Information Theory, Vol. 32, pp. 276-282, 1986.

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Meisters, G., Principal vertices, exposed points, and ears, American Mathematical Monthly. April 1980, 284-285.

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Mirzaian, A., Hamiltonian triangulations and circumscribing polygons of disjoint line segments, Computational Geometry: Theory and Applications, 2 (1992) 15-30.

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Urrutia, J., Art Gallery and Illumination Problems, in Handbook on Computational Geometry, J. Sac, and J. Urrutia, (eds.), Elsevier Science Publishers, Amsterdam, 2000, p. 973-1027.

Urrutia, J., Sixth proof of the orthogonal art gallery theorem (unpublished manuscript).

Valtr, P., Guarding galleries where no point sees a small area, Israel J. Math., 104 (1998) 1-16.

Viswanathan, S., Tight bounds for the number of edge guards for spiral polygons, J. Geom., 51 (1994) 178-186.

Zalik, B. and G. Clapworthy, A universal trapezoidation algorithm for planar polygons, Computers & Graphs, 23 (1999) 353-363.

Zalik, B. and A. Jezernik, K. Zalik, Polygon trapezoidation by sets of open trapezoids, Computers & Graphics, 27 (2003) 791-800.


The Association for Computing Machines via its special interest groups for Graphics and Algorithms and Computation Theory sponsors an annual meeting on Computational Geometry. The proceedings of this conference has been published every year since the first conference was held in 1985. Papers in these volumes can be accessed via the ACM Portal.

Those who can access JSTOR can find some of the papers mentioned above there. For those with access, the American Mathematical Society's MathSciNet can be used to get additional bibliographic information and reviews of some these materials.

  1. Introduction
  2. What is a diagonal?
  3. Triangulations and ears
  4. Art gallery theorems
  5. Where do new problems come from?
  6. References

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