Comparison of convex hulls and box hulls. (English) Zbl 1157.52304

Boros, Endre; Gurvich, Vladimir; Liu, Ying

Ars Comb. 77, 193-204 (2005).

A convex hull of a set of points \(X\) is the minimal convex set containing \(X\). A box is a set of the form \(B=\{\vec x\in \mathbb{R}^d \mid \vec a \leq \vec x \leq \vec b\}\) where \(\vec a\) and \(\vec b\) are vectors in \(\mathbb{R}^d\) and the inequalities hold component-wise. A box hull of set of points \(X\) is the minimal box containing \(X\).
The paper describes several Helly-type theorems for box hulls.

Reviewer: Petr Kolman (Praha)

MSC:

52A35	Helly-type theorems and geometric transversal theory
52A20	Convex sets in \(n\) dimensions (including convex hypersurfaces)

Keywords:

convex hull; convex box; Helly-type theorems