Almost tight bounds for &egr;-nets
Discrete & Computational Geometry
Computing Many Faces in Arrangements of Lines and Segments
SIAM Journal on Computing
Dynamic data structures for fat objects and their applications
Computational Geometry: Theory and Applications
Lectures on Discrete Geometry
Polynomial-time approximation schemes for packing and piercing fat objects
Journal of Algorithms
New Constructions of Weak ε-Nets
Discrete & Computational Geometry
The Complexity of the Union of $(\alpha,\beta)$-Covered Objects
SIAM Journal on Computing
Improved Approximation Algorithms for Geometric Set Cover
Discrete & Computational Geometry
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Improved Bounds on the Union Complexity of Fat Objects
Discrete & Computational Geometry
Efficient Colored Orthogonal Range Counting
SIAM Journal on Computing
Small-size ε-nets for axis-parallel rectangles and boxes
Proceedings of the forty-first annual ACM symposium on Theory of computing
Lower bounds for weak epsilon-nets and stair-convexity
Proceedings of the twenty-fifth annual symposium on Computational geometry
A Non-linear Lower Bound for Planar Epsilon-Nets
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Tight lower bounds for the size of epsilon-nets
Proceedings of the twenty-seventh annual symposium on Computational geometry
| Hi-index | 0.89 |
We show the existence of weak @e-nets of size O(1/@eloglog(1/@e)) for point sets and axis-parallel boxes in R^d, for d=4. Our analysis uses a non-trivial variant of the recent technique of Aronov et al. (2009) [3] that yields (strong) @e-nets, whose size have the above asymptotic bound, for d=2,3.