Piercing pairwise intersecting geodesic disks by five points

A. Karim Abu-Affash, Meytal Maman, Paz Carmi

Research output: Contribution to journalArticlepeer-review

20 Downloads (Pure)


Given a simple polygon P on n vertices and a set D of m pairwise intersecting geodesic disks in P, we show that five points in P are always sufficient to pierce all the disks in D. The points can be computed in O((n+m)log⁡nr) time, where nr is the number of the reflex vertices of P. This improves the previous bound of 14, obtained by Bose, Carmi, and Shermer.

Original languageEnglish
Article number101947
JournalComputational Geometry: Theory and Applications
StatePublished - 1 Feb 2023


  • Geodesic disk
  • Helly's theorem
  • Piercing set
  • Simple polygon

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics


Dive into the research topics of 'Piercing pairwise intersecting geodesic disks by five points'. Together they form a unique fingerprint.

Cite this