Voronoi diagrams and arrangements
Discrete & Computational Geometry
A general approach to d-dimensional geometric queries
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
A deterministic algorithm for partitioning arrangements of lines and its application
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
Quasi-optimal range searching in spaces of finite VC-dimension
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Some new bounds for Epsilon-nets
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Some new bounds for Epsilon-nets
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Almost optimal set covers in finite VC-dimension: (preliminary version)
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Parallel Convex Hull Computation by Generalised Regular Sampling
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
Improved approximation algorithms for geometric set cover
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Improved approximation algorithms for connected sensor cover
Wireless Networks
Succinct approximate convex pareto curves
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient data dissemination using locale covers
Pervasive and Mobile Computing
Self-improving algorithms for delaunay triangulations
Proceedings of the twenty-fourth annual symposium on Computational geometry
Proceedings of the twenty-fourth annual symposium on Computational geometry
Minimizing interference of a wireless ad-hoc network in a plane
Theoretical Computer Science
Small-size ε-nets for axis-parallel rectangles and boxes
Proceedings of the forty-first annual ACM symposium on Theory of computing
Epsilon nets and union complexity
Proceedings of the twenty-fifth annual symposium on Computational geometry
PTAS for geometric hitting set problems via local search
Proceedings of the twenty-fifth annual symposium on Computational geometry
Near-linear approximation algorithms for geometric hitting sets
Proceedings of the twenty-fifth annual symposium on Computational geometry
ε-Net Approach to Sensor k-Coverage
WASA '09 Proceedings of the 4th International Conference on Wireless Algorithms, Systems, and Applications
Ɛ-net approach to sensor k-coverage
EURASIP Journal on Wireless Communications and Networking - Special issue on wireless network algorithms, systems, and applications
Small-Size $\eps$-Nets for Axis-Parallel Rectangles and Boxes
SIAM Journal on Computing
Tight lower bounds for the size of epsilon-nets
Proceedings of the twenty-seventh annual symposium on Computational geometry
SIAM Journal on Computing
Towards faster linear-sized nets for axis-aligned boxes in the plane
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
Approximately dominating representatives
ICDT'05 Proceedings of the 10th international conference on Database Theory
Minimizing interference of a wireless ad-hoc network in a plane
ALGOSENSORS'06 Proceedings of the Second international conference on Algorithmic Aspects of Wireless Sensor Networks
Coloring planar homothets and three-dimensional hypergraphs
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Small-size relative (p,ε)-approximations for well-behaved range spaces
Proceedings of the twenty-ninth annual symposium on Computational geometry
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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.