论文信息 - Piercing Pairwise Intersecting Geodesic Disks by Five Points

Piercing Pairwise Intersecting Geodesic Disks by Five Points

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. This improves the previous bound of 14, obtained by Bose, Carmi, and Shermer [1].

[1] E. Helly,et al. Über Systeme von abgeschlossenen Mengen mit gemeinschaftlichen Punkten , 1930 .

[2] Pat Morin,et al. Stabbing Pairwise Intersecting Disks by Four Points , 2018, Discrete & Computational Geometry.

[3] E. Helly. Über Mengen konvexer Körper mit gemeinschaftlichen Punkte. , 1923 .

[4] Micha Sharir,et al. Computing the geodesic center of a simple polygon , 1989, Discret. Comput. Geom..

[5] Prosenjit Bose,et al. Piercing pairwise intersecting geodesic disks , 2021, Comput. Geom..

[6] Haim Kaplan,et al. Stabbing pairwise intersecting disks by five points , 2018, ISAAC.