Add to ORKGWe show the existence of weak ε-nets of size O (1/ε log log (1/ε)) for point sets and axis-parallel boxes in Rd, for d ≥ 4. Our analysis uses a non-trivial variant of the recent technique of Aronov et al. [2] that yields (strong) ε-nets, whose size have the above asymptotic bound, for d = 2, 3
This thesis deals with strong and weak -nets in geometry and related problems. In the first half of...
We prove that there exist no weak ε-nets of constant size for lines and convex sets in ℝ^d
A finite set $N \subset \R^d$ is a {\em weak $\eps$-net} for an $n$-point set $X\subset \R^d$ (with ...
Let B be any set of n axis-aligned boxes in R d, d ≥ 1. We call a subset N ⊆ B a(1/c)-net for B if a...
Given a set P of n points in Rd and $\epsilon$ > 0, we consider the problem of constructing weak $\e...
AbstractGiven a set P of n points in Rd and ϵ>0, we consider the problem of constructing weak ϵ-nets...
Given a set P of n points in Rd and $\epsilon$ > 0, we consider the problem of constructing weak $\...
AbstractGiven a set P of n points in Rd and ϵ>0, we consider the problem of constructing weak ϵ-nets...
We study the problem of finding small weak ε-nets in three dimensions and provide new upper and lowe...
Given a family B of axis-parallel boxes in Rd, let τ denote its piercing number, and ν its independe...
In the plane, we can find a weak "-net for convex sets consisting of O(" \Gamma2 ) point...
International audienceFollowing groundbreaking work by Haussler and Welzl (1987), the use of small-n...
Let B be any set of n axis-aligned boxes in Rd, d ≥ 1. For any point p, we define the subset Bp of B...
Let P be a set of n points in R-d. A point x is said to be a centerpoint of P if x is contained in e...
AbstractGiven a set P of points in the plane, a set of points Q is a weak ε-net with respect to a fa...
This thesis deals with strong and weak -nets in geometry and related problems. In the first half of...
We prove that there exist no weak ε-nets of constant size for lines and convex sets in ℝ^d
A finite set $N \subset \R^d$ is a {\em weak $\eps$-net} for an $n$-point set $X\subset \R^d$ (with ...
Let B be any set of n axis-aligned boxes in R d, d ≥ 1. We call a subset N ⊆ B a(1/c)-net for B if a...
Given a set P of n points in Rd and $\epsilon$ > 0, we consider the problem of constructing weak $\e...
AbstractGiven a set P of n points in Rd and ϵ>0, we consider the problem of constructing weak ϵ-nets...
Given a set P of n points in Rd and $\epsilon$ > 0, we consider the problem of constructing weak $\...
AbstractGiven a set P of n points in Rd and ϵ>0, we consider the problem of constructing weak ϵ-nets...
We study the problem of finding small weak ε-nets in three dimensions and provide new upper and lowe...
Given a family B of axis-parallel boxes in Rd, let τ denote its piercing number, and ν its independe...
In the plane, we can find a weak "-net for convex sets consisting of O(" \Gamma2 ) point...
International audienceFollowing groundbreaking work by Haussler and Welzl (1987), the use of small-n...
Let B be any set of n axis-aligned boxes in Rd, d ≥ 1. For any point p, we define the subset Bp of B...
Let P be a set of n points in R-d. A point x is said to be a centerpoint of P if x is contained in e...
AbstractGiven a set P of points in the plane, a set of points Q is a weak ε-net with respect to a fa...
This thesis deals with strong and weak -nets in geometry and related problems. In the first half of...
We prove that there exist no weak ε-nets of constant size for lines and convex sets in ℝ^d
A finite set $N \subset \R^d$ is a {\em weak $\eps$-net} for an $n$-point set $X\subset \R^d$ (with ...