On Separating Points by Lines

Sariel Har-Peled, Mitchell Jones

Research output: Contribution to journalArticlepeer-review


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, denoted by sep (P). We show that the minimum number of lines needed to separate n points, picked randomly (and uniformly) in the unit square, is Θ ~ (n2 / 3) , where Θ ~ hides polylogarithmic factors. In addition, we provide a fast O(log (sep (P))) -approximation algorithm for computing the separability of a given point set in the plane. Finally, we point out the connection between separability and partitions.

Original languageEnglish (US)
Pages (from-to)705-730
Number of pages26
JournalDiscrete and Computational Geometry
Issue number3
StatePublished - Apr 1 2020

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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