# On Separating Points by Lines

arXiv: https://arxiv.org/abs/1706.02004 · HTML: https://mlsanity.com/paper/1706.02004/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2017.

## Built on by (most cited first, 1 of 1)

- [Time to Spike? Understanding the Representational Power of Spiking Neural Networks in Discrete Time](https://mlsanity.com/paper/2505.18023/) (2025)

## Abstract (arXiv)

Given a set P of n 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 n points, picked randomly (and uniformly) in the unit square, is Theta( n2/3), where 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.