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The interface between computational and combinatorial geometry
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Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms table of contents
Vancouver, British Columbia
SESSION: Session 2:Invited Plenary Abstract table of contents
Pages: 137 - 145  
Year of Publication: 2005
ISBN:0-89871-585-7
Author
Micha Sharir  Tel Aviv University, Tel Aviv, Israel
Sponsors
SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
: SIAM Activity Group on Discrete Mathematics
Publisher
Society for Industrial and Applied Mathematics  Philadelphia, PA, USA
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ABSTRACT

We illustrate the rich interface between computational and combinatorial geometry by a series of examples, including k-sets, randomized incremental algorithms, random sampling and partitioning, and analysis of geometric arrangements.


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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P. Agarwal and M. Sharir, Davenport-Schinzel sequences and their geometric applications, in Handbook of Computational Geometry, J. R. Sack and J. Urrutia (Eds.), North-Holland, 2000, 1--47.
 
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P. Agarwal and M. Sharir, Arrangements of surfaces in higher dimensions, in Handbook of Computational Geometry, J. R. Sack and J. Urrutia (Eds.), North-Holland, 2000, 49--119.
 
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F. Aurenhammer and R. Klein, Voronoi diagrams, in Handbook of Computational Geometry, J.-R. Sack and J. Urrutia, Eds., Elsevier North Holland, 2000, pp. 201--290.
 
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S. Basu, On the combinatorial and topological complexity of a single cell, Discrete Comput. Geom. 29 (2003), 41--59.
 
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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 (1998), 485--519.
 
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T. M. Chan, On levels in arrangements of curves, Discrete Comput. Geom. 29 (2003), 375--393.
 
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T. K. Dey, Improved bounds for planar k-sets and related problems, Discrete Comput. Geom. 19 (1998), 373--382.
 
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A. Efrat and M. Sharir, The complexity of the union of fat objects in the plane, Discrete Comput. Geom.. 23 (2000), 171--189.
 
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L. Guibas, D. E. Knuth and M. Sharir, Randomized incremental construction of Voronoi and Delaunay diagrams, Algorithmica 7 (1992), 381--413.
 
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D. Halperin and M. Sharir, New bounds for lower envelopes in three dimensions with applications to visibility of terrains, Discrete Comput. Geom. 12 (1994), 313--326.
 
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D. Halperin and M. Sharir, Almost tight upper bounds for the single cell and zone problems in three dimensions, Discrete Comput. Geom. 14 (1995), 385--410.
 
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V. Koltun and M. Sharir, Polyhedral Voronoi diagrams of polyhedra in three dimensions, Discrete Comput. Geom. 31 (2004), 83--124.
 
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J. Pach, I. Safruti and M. Sharir, The union of congruent cubes in three dimensions, Discrete Comput. Geom. 30 (2003), 133--160.
 
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J. Pach and M. Sharir, Geometric incidences, in Towards a Theory of Geometric Graphs (J. Pach, ed.), Contemporary Mathematics, Vol. 342, Amer. Math. Soc., Providence, RI, 2004, pp. 185--223.
 
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M. Sharir, Motion planning, in Handbook of Discrete and Computational Geometry, 2nd Edition (J. E. Goodman and J. O'Rourke, Eds.), CRC Press, Boca Raton, Fla., 2004, 1037--1064.
 
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M. Sharir, Arrangements of surfaces in higher dimensions, in Advances in Discrete and Computational Geometry (Proc. 1996 AMS Mt. Holyoke Summer Research Conference, B. Chazelle, J. E. Goodman and R. Pollack, Eds.) Contemporary Mathematics No. 223, American Mathematical Society, 1999, 335--353.
 
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