Abstract
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)lognr) 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 language | English |
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Article number | 101947 |
Journal | Computational Geometry: Theory and Applications |
Volume | 109 |
DOIs | |
State | Published - 1 Feb 2023 |
Keywords
- 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