Modem Illumination of Monotone Polygons (2009)
Oswin Aichholzer, Ruy Fabila-monroy, David Flores-peñaloza, Thomas Hackl, Clemens Huemer, Jorge Urrutia, ...
We study a generalization of the classical problem of illumination of polygons. Instead of modeling a light source we model a wireless device whose radio signal can penetrate a given number k of...
Maximizing Maximal Angles for Plane Straight-Line Graphs ⋆ (2009)
Oswin Aichholzer, Thomas Hackl, Michael Hoffmann, Clemens Huemer, Attila Pór, Francisco Santos, ...
Abstract. Let G =(S, E) be a plane straight-line graph on a finite point set S ⊂ R 2 in general position. The incident angles of a point p ∈ S in G are the angles between any two edges of G that...
Lower and upper bounds on the number of empty cylinders and ellipsoids (2009)
Aichholzer, Oswin, Aurenhammer, Franz, Devillers, Olivier, Hackl, Thomas, Teillaud, Monique, Vogtenhuber, Birgit
Given a set S of n points in three dimensions, we study the maximum numbers of quadrics spanned by subsets of points in S in several ways. Among various results we prove that the number of empty...
Lower and upper bounds on the number of empty cylinders and ellipsoids (2009)
Aichholzer, Oswin, Aurenhammer, Franz, Devillers, Olivier, Hackl, Thomas, Teillaud, Monique, Vogtenhuber, Birgit
Given a set S of n points in three dimensions, we study the maximum numbers of quadrics spanned by subsets of points in S in several ways. Among various results we prove that the number of empty...
Oswin Aichholzer, Thomas Hackl, Birgit Vogtenhuber, Clemens Huemer, Ferran Hurtado, Hannes Krasser
We investigate the number of plane geometric, i.e., straight-line, graphs, a set S of n points in the plane admits. We show that the number of plane graphs and connected plane graphs as well as the...
Abstract Pointed Drawings of Planar Graphs (2008)
Oswin Aichholzer, Günter Rote, André Schulz, Birgit Vogtenhuber
We study the problem how to draw a planar graph such that every vertex is incident to an angle greater than π. In general a straight-line embedding cannot guarantee this property. We present...
Counting Quadrics and Delaunay Triangulations and a new Convex Hull Theorem (2008)
Aicholzer, Oswin, Devillers, Olivier, Aurenhammer, Franz, Hackl, Thomas, Teillaud, Monique, Vogtenhuber, Birgit
Given a set $\cal S$ of $n$ points in three dimensions, we study the maximum numbers of quadrics spanned by subsets of points in $\cal S$ in various ways. We prove that the set of empty or enclosing...
Counting Quadrics and Delaunay Triangulations and a new Convex Hull Theorem (2008)
Aicholzer, Oswin, Devillers, Olivier, Aurenhammer, Franz, Hackl, Thomas, Teillaud, Monique, Vogtenhuber, Birgit
Given a set $\cal S$ of $n$ points in three dimensions, we study the maximum numbers of quadrics spanned by subsets of points in $\cal S$ in various ways. We prove that the set of empty or enclosing...
Pointed Drawings of Planar Graphs (2008)
Oswin Aichholzer, Günter Rote, André Schulz, Birgit Vogtenhuber
We study the problem how to draw a planar graph such that every vertex is incident to an angle greater than π. In general a straightline embedding cannot guarantee this property. We present...
Matching edges and faces in polygonal partitions (2008)
Aichholzer, Oswin, Aurenhammer, Franz, Gonzalez-Nava, Paola, Hackl, Thomas, Huerner, Clemens, Hurtado, Ferran, ...
Maximizing Maximal Angles for Plane Straight-Line Graphs (2007)
Aichholzer, Oswin, Hackl, Thomas, Hoffmann, Michael, Huemer, Clemens, Por, Attila, Santos, Francisco, ...
Let $G=(S, E)$ be a plane straight-line graph on a finite point set $S\subset\R^2$ in general position. The \emph{incident angles} of a point $p \in S$ in $G$ are the angles between any two edges of...
On the number of plane graphs (2006)
Oswin Aichholzer, Thomas Hackl, Clemens Huemer, Ferran Hurtado, Hannes Krasser, Birgit Vogtenhuber
We investigate the number of plane geometric, i.e., straight-line, graphs, a set S of n points in the plane admits. We show that the number of plane graphs is minimized when S is in convex position,...
O. Aichholzer, T. Hackl, C. Huemer, F. Hurtado, H. Krasser, B. Vogtenhuber, ...
We investigate the number of plane geometric, i.e., straight-line, graphs, a set S of n points in the plane admits. We show that the number of plane geometric graphs and connected plane geometric...