English

On Separating Points by Lines

Computational Geometry 2017-06-08 v1

Abstract

Given a set PP of nn points in the plane, its separability is the minimum number of lines needed to separate all its pairs of points from each other. We show that the minimum number of lines needed to separate nn points, picked randomly (and uniformly) in the unit square, is Θ(n2/3)\Theta( n^{2/3}), where Θ\Theta hides polylogarithmic factors. In addition, we provide a fast approximation algorithm for computing the separability of a given point set in the plane. Finally, we point out the connection between separability and partitions.

Keywords

Cite

@article{arxiv.1706.02004,
  title  = {On Separating Points by Lines},
  author = {Sariel Har-Peled and Mitchell Jones},
  journal= {arXiv preprint arXiv:1706.02004},
  year   = {2017}
}