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Computational geometry
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Volume 32 ,  Issue 3  (September 2001) table of contents
Pages: 63 - 72  
Year of Publication: 2001
ISSN:0163-5700
Authors
Joseph S. B. Mitchell  Univ. at Stony Brook, Stony Brook, NY
Joseph O'Rourke  Smith College, Northampton, MA
Publisher
ACM  New York, NY, USA
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ABSTRACT

A compendium of thirty previously published open problems in computational geometry is presented


REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

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G. Albers, L. J. Guibas, J. S. B. Mitchell, and T. Roos. Voronoi diagrams of moving points. Internat. J. Comput. Geom. Appl., 8:365-380, 1998.
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E. M. Arkin, M. Held, J. S. B. Mitchell, and s. S. Skiena. Hamiltonian triangulations for fast rendering. Visual Comput., 12(9): 429-444, 1996.
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P. K. Agarwal and M. Sharir. Davenport-Schinzel sequences and their geometric applications. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 1-47. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
 
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P. K. Agarwal and M. Sharir. Pipes, cigars, and kreplach: The union of Minkowski sums in three dimensions. Discrete Comput. Geom. 24(4): 645-685, 2000.
 
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P. K. Agarwal and K. R. Varadarajan. Approximating monotone polygonal curves using the uniform metric. Discrete Comput. Geom., 23, 2000. to appear.
 
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M. Bern, D. Eppstein, P. K. Agarwal, N. Amenta, P. Chew, T. Dey, D. P. Dobkin, H. Edelsbrunner, C. Grimm, L. J. Guibas, J. Harer, J. Hass, A. Hicks, C. K. Johnson, G. Lerman, D. Letscher, P. Plassmann, E. Sedgeick, J. Snoeyink, J. Weeks, C. Yap, and D. Zorin. Emerging challenges in computational topology, 1999. Report on an NSF Workshop on computational Topology, June 11-12, Miami Beach, FL
 
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H. Brönnimann and M. T. Goodrich. Almost optimal set covers in finite VC-dimension. Discrete Comput. Geom., 14: 263-279, 1995.
 
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M. Bern and A. Sahai. Pushing disks together — The continuous-motion case. Discrete Comput. Geom., 20: 299-514, 1998.
 
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J.-D. Boissonnat, M. Sharir, B. Tagansky, and M. Yvinec. Voronoi diagrams in higher dimensions under certain polyhedral distance functions. Discrete Comput. Geom., 19(4): 473-484, 1998.
 
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W. S. Chan and F. Chin. Approximation of polygonal curves with minimum number of line segments or minimum error. Internat. J. Comput. Geom. Appl., 6:59-77, 1996.
 
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B. Chazelle. Tight bounds on the stabbing number of spanning trees in Euclidean space. Report CS-TR-155-88, Dept. Comput. Sci., Princeton Univ., Princeton, NJ, 1988.
 
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T. M. Chan. Output-sensitive results on convex hulls, extreme points, and related problems. Discrete Comput. Geom., 16:369-387, 1996.
 
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T. K. Dey. Improved bounds on planar k-sets and related problems. Discrete Comput. Geom., 19:373-382, 1998.
 
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D. Eppstein. Approximating the minimum weight Steiner triangulation. Discrete Comput. Geom., 11:163-191, 1994.
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A. Efrat and M. Sharir. On the complexity of the union of fat objects in the plane. Discrete Comput. Geom., 23:171-189, 2000.
 
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S. Kapoor, S. N. Maheshwari, and J. S. B, Mitchell. An efficient algorithm for Euclidean shortest paths among polygonal obstacles in the plane Discrete Comput. Geom., 18:377-383, 1997.
 
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J. S. B. Mitchell. Geometric shortest paths and network optimization. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 633-701. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
 
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J. S. B. Mitchell, G. Rote, and G. Woeginer. Minimum-link paths among obstacles in the plane. Algorithmica, 8:431-459, 1992
 
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J. Matoušek, M. Sharir, and E. Welzl. A subexponential bound for linear programming. Algorithmica, 16:498-516, 1996.
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M. Sharir. Almost tight upper bounds for lower envelopes in higher dimensions. Discrete Comput. Geom. , 12:327-345, 1994.
 
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J. Urrutia. Art gallery and illumination problems. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry pages 973-1027, North-Holland, 2000.
 
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E. Welzl. Geometric graphs with small stabbing numbers: Combinatorics and applications. In Proc 9th Internat. Conf. Fund. Comput. Theory, Lecture Notes Comput. Sci., Springer-Verlag, 1993.
 
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Collaborative Colleagues:
Joseph S. B. Mitchell: colleagues
Joseph O'Rourke: colleagues