Large convex holes in random point sets

Abstract

A convex hole (or empty convex polygon) of a point set P in the plane is a convex polygon with vertices in P , containing no points of P in its interior. Let R be a bounded convex region in the plane. We show that the expected number of vertices of the largest convex hole of a set of n random points chosen independently and uniformly over R is Θ(logn/(log log n)), regardless of the shape of R.

DOI: 10.1016/j.comgeo.2012.11.004

Extracted Key Phrases

1 Figure or Table

Cite this paper

@article{Balogh2013LargeCH, title={Large convex holes in random point sets}, author={J{\'o}zsef Balogh and Hern{\'a}n Gonz{\'a}lez-Aguilar and Gelasio Salazar}, journal={Comput. Geom.}, year={2013}, volume={46}, pages={725-733} }