Jun 5, 2012 · 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 ...

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.

Jun 13, 2015 · Abstract:Let K, L be convex sets in the plane. For normalization purposes, suppose that the area of K is 1. Suppose that a set K_n of n ...

It is shown that with high probability the largest area of a hole homothetic to L is ( 1 + o ( 1 ) ) log ⁡ n / n .

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 ...

Regarding the area of the largest convex hole, we give an answer that is asymp- totically tight within a factor of 4: Theorem 1.2. Let K be a convex set in the ...

Sep 6, 2021 · Does a random set of points in the plane contain a large empty convex polygon? ... Large convex holes in random point sets, Comput. Geom. 46, No.

Nov 5, 2012 · 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.

Sep 23, 2012 · If a set of points is not in convex position, then some convex combination of them equals another point in the set, and this is true for their ...

Large convex holes in random point sets · J. Balogh, H. González-Aguilar, G. Salazar · Published in Computational geometry 5 June 2012 · Computer Science, ...