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 [1].
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