Uniformly Discrete Forests with Poor Visibility
Noga Alon · Combinatorics Probability Computing · 2017
We prove that there is a setFin the plane so that the distance between any two points ofFis at least 1, and for any positive ϵ < 1, and every line segment in the plane of length at least ϵ−1−o(1), there is a point ofFwithin distance ϵ of the segment. This is tight up to theo(1)-term in the exponent, improving earlier estimates of Peres, of Solomon and Weiss, and of Adiceam.