How to net a lot with little: small &egr;-nets for disks and halfspaces

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How to net a lot with little: small &egr;-nets for disks and halfspaces

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Annual Symposium on Computational Geometry archive
Proceedings of the sixth annual symposium on Computational geometry table of contents

Berkley, California, United States

Pages: 16 - 22

Year of Publication: 1990

ISBN:0-89791-362-0

Authors

Jiří Matoušek	Department of Computer Science, Charles University, Malostranské nám. 25, 118 00 Praha 1, Czechoslovakia
Raimund Seidel	Computer Science Division, University of California, Berkeley, Berkeley, CA
E. Welzl	Fachbereich Mathematik, Freie Universität Berlin, Arnimallee 2-6, D-1000 Berlin 33, West Germany

Sponsors

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

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ACM New York, NY, USA

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Downloads (6 Weeks): 4, Downloads (12 Months): 22, Citation Count: 13

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ABSTRACT

It is known that in general range spaces of VC-dimension d > 1 require &egr;-nets to be of size at least &OHgr;(d/&egr; log 1/&egr;). We investigate the question whether this general lower bound is valid for the special range spaces that typically arise in computational geometry. We show that disks and pseudo-disks in the plane as well as halfspaces in R3 allow &egr;-nets of size only &Ogr;(1/&egr;), which is best possible up to a multiplicative constant. The analogous questions for higher-dimensional spaces remain open.

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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	János Pach , Gerhard Woeginger, Some new bounds for Epsilon-nets, Proceedings of the sixth annual symposium on Computational geometry, p.10-15, June 07-09, 1990, Berkley, California, United States
	Kenneth L. Clarkson , Kasturi Varadarajan, Improved approximation algorithms for geometric set cover, Proceedings of the twenty-first annual symposium on Computational geometry, June 06-08, 2005, Pisa, Italy
	Magnús M. Halldórsson , Takeshi Tokuyama, Minimizing interference of a wireless ad-hoc network in a plane, Theoretical Computer Science, v.402 n.1, p.29-42, July, 2008
	Stefan Funke , Alex Kesselman , Fabian Kuhn , Zvi Lotker , Michael Segal, Improved approximation algorithms for connected sensor cover, Wireless Networks, v.13 n.2, p.153-164, April 2007
	Ilias Diakonikolas , Mihalis Yannakakis, Succinct approximate convex pareto curves, Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms, p.74-83, January 20-22, 2008, San Francisco, California
	Kenneth L. Clarkson , C. Seshadhri, Self-improving algorithms for delaunay triangulations, Proceedings of the twenty-fourth annual symposium on Computational geometry, June 09-11, 2008, College Park, MD, USA
	Sandeep Gupta , Jinfeng Ni , Chinya V. Ravishankar, Efficient data dissemination using locale covers, Pervasive and Mobile Computing, v.4 n.2, p.254-275, April, 2008
	Evangelia Pyrga , Saurabh Ray, New existence proofs ε-nets, Proceedings of the twenty-fourth annual symposium on Computational geometry, June 09-11, 2008, College Park, MD, USA
	Pankaj K. Agarwal , Esther Ezra , Micha Shair, Near-linear approximation algorithms for geometric hitting sets, Proceedings of the 25th annual symposium on Computational geometry, June 08-10, 2009, Aarhus, Denmark
	Nabil Hassan Mustafa , Saurabh Ray, PTAS for geometric hitting set problems via local search, Proceedings of the 25th annual symposium on Computational geometry, June 08-10, 2009, Aarhus, Denmark
	Boris Aronov , Esther Ezra , Micha Shair, Small-size ε-nets for axis-parallel rectangles and boxes, Proceedings of the 41st annual ACM symposium on Theory of computing, May 31-June 02, 2009, Bethesda, MD, USA
	Kasturi Varadarajan, Epsilon nets and union complexity, Proceedings of the 25th annual symposium on Computational geometry, June 08-10, 2009, Aarhus, Denmark