New constructions of weak epsilon-nets

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2003, Pages 129-135

  Matoušek, Jǐrí ^a   Wagner, Uli ^b  

^a CHARLES UNIVERSITY   (Czech Republic)

^b ETH ZURICH   (Switzerland)

Author keywords

Weak Epsilon Nets

Indexed keywords

ALGORITHMS; GEOMETRY; THEOREM PROVING;

CONVEX SETS;

SET THEORY;

EID: 0038714815     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (13)

1. Pankaj K. Agarwal and Jiří Matoušek. On range searching with semialgebraic sets. Discrete Comput. Geom., 11:393-418, 1994.
2. Noga Alon, Imre Bárány, Zoltán Füredi, and Daniel Kleitman. Point selections and weak ε-nets for convex hulls. Combin. Probab. Comput., 1(3):103-112, 1992.
3. Noga Alon and Daniel J. Kleitman. Piercing convex sets and the Hadwiger-Debrunner (p,q)-problem. Adv. Math., 96(1):103-112, 1992.
4. Boris Aronov, Marco Pellegrini, and Micha Sharir. On the zone of a surface in a hyperplane arrangement. Discrete Comput. Geom., 9(2):177-186, 1993.
5. Jacek Bochnak, Michel Coste, and Marie Françoise Roy. Real Algebraic Geometry. Springer-Verlag, New York, 1998.
6. Bernard Chazelle, Herbert Edelsbrunner, David Eppstein, Michelangelo Grigni, Leonidas Guibas, Micha Sharir, and Emo Welzl. Algorithms for weak epsilon-nets. Manuscript, 1995, available at http://citeseer.nj.nec.com/24190.html.
7. Bernard Chazelle, Herbert Edelsbrunner, Michelangelo Grigni, Leonidas J. Guibas, Micha Sharir, and Emo Welzl. Improved bounds on weak ε-nets for convex sets. Discrete Comput. Geom., 13:1-15., 1995.
8. Bernard Chazelle, Herbert Edelsbrunner. Leonidas Guibas, and Micha Sharir. A singly-exponential stratification scheme for real semi-algebraic varieties and its applications. In Proc. 16th Internat. Colloq. Automata Lang. Program., volume 372 of Lecture Notes Comput. Sci., pages 179-192. Springer-Verlag, Berlin etc., 1989.
9. David Haussler and Emo Welzl. ε-Nets and Simplex Range Queries. Discrete Comput. Geom., 2:127-151, 1987.
10. Vladlen Koltun. Almost tight upper bounds for vertical decompositions in four dimensions. In Proc. 42nd IEEE Symposium on Foundations of Computer Science, pages 56-65, 2001.
11. Jiří Matoušek. Efficient partition trees. Discrete Comput. Geom., 8(3):315-334, 1992.
12. Jiří Matoušek. Lectures on Discrete Geometry.Springer-Verlag, New York, 2002.
13. Jiří Matoušek. A lower bound for weak ε-nets in high dimension. Discrete Comput. Geom., 28:45-48, 2002.