An optimal generalization of the centerpoint theorem, and its extensions
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Weak ε-nets have basis of size o(1/ε log (1/ε)) in any dimension
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Weak ε-nets have basis of size O (1/εlog(1/ε)) in any dimension
Computational Geometry: Theory and Applications
Weak ε-nets and interval chains
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Weak ε-nets and interval chains
Journal of the ACM (JACM)
An optimal extension of the centerpoint theorem
Computational Geometry: Theory and Applications
Lower bounds for weak epsilon-nets and stair-convexity
Proceedings of the twenty-fifth annual symposium on Computational geometry
Reprint of: Weak ε-nets have basis of size O(1/εlog(1/ε) ) in any dimension
Computational Geometry: Theory and Applications
Centerpoints and Tverberg's technique
Computational Geometry: Theory and Applications
A note about weak ε-nets for axis-parallel boxes in d-space
Information Processing Letters
A randomised approximation algorithm for the partial vertex cover problem in hypergraphs
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
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A finite set $N \subset \R^d$ is a {\em weak $\eps$-net} for an $n$-point set $X\subset \R^d$ (with respect to convex sets) if $N$ intersects every convex set $K$ with $|K\,\cap\,X|\geq \eps n$. We give an alternative, and arguably simpler, proof of the fact, first shown by Chazelle et al., that every point set $X$ in $\R^d$ admits a weak $\eps$-net of cardinality $O(\eps^{-d}\polylog(1/\eps))$. Moreover, for a number of special point sets (e.g., for points on the moment curve), our method gives substantially better bounds. The construction yields an algorithm to construct such weak $\eps$-nets in time $O(n\ln(1/\eps))$.