Computing k-Centers On a Line (2009)
Brass, Peter, Knauer, Christian, Na, Hyeon-Suk, Shin, Chan-Su, Vigneron, Antoine
In this paper we consider several instances of the k-center on a line problem where the goal is, given a set of points S in the plane and a parameter k >= 1, to find k disks with centers on a line l...
A Lower Bound on the Area of a 3-Coloured Disk Packing (2008)
Brass, Peter, Hurtado, Ferran, Lafreniere, Benjamin, Lubiw, Anna
Given a set of unit-disks in the plane with union area $A$, what fraction of $A$ can be covered by selecting a pairwise disjoint subset of the disks? Rado conjectured 1/4 and proved $1/4.41$....
On the Size of Higher-Dimensional (2008)
Abstract. I show that there are sets of n points in three dimensions, in general position, such that any triangulation of these points has only O(n 5/3) simplices. This is the first nontrivial upper...
Constructing Optimal Highways ∗ Hee-Kap Ahn † Helmut Alt ‡ Tetsuo Asano § Sang Won Bae (2008)
Peter Brass, Otfried Cheong, Christian Knauer, Hyeon-suk Na, Chan-su Shin
On k + -neighbour packings and one-sided Hadwiger configurations, Beiträge zur Alg. und Geom (2008)
Abstract. We show that in d-dimensional Euclidean space the maximum number of non-overlapping translates of a d-dimensional convex body K that can touch K and can lie in a closed supporting...
Hee-kap Ahn, Peter Brass, Otfried Cheong, Hyeon-suk Na, Chan-su Shin, Antoine Vigneron
Given a planar convex set C, we give sublinear approximation algorithms to determine approximations of the largest axially symmetric convex set S contained in P, and the smallest such set S ′ that...
Constructing Optimal Highways ∗ Hee-Kap Ahn † Helmut Alt ‡ Tetsuo Asano § Sang Won Bae (2008)
Peter Brass, Otfried Cheong, Christian Knauer, Hyeon-suk Na, Chan-su Shin
Constructing Optimal Highways (2007)
Ahn, Hee-Kap, Alt, Helmut, Asano, Tetsuo, Bae, Sang Won, Brass, Peter, Cheong, Otfried, ...
For two points $p$ and $q$ in the plane, a straight line $h$, called a highway, and a real $v>1$, we define the \emph{travel time} (also known as the \emph{city distance}) from $p$ and $q$ to be the...
Ahn, Hee-Kap, Brass, Peter, Cheong, Otfried, Na, Hyeon-Suk, Shin, Chan-Su, Vigneron, Antoine
Given a planar convex set C, we give sublinear approximation algorithms to determine approximations of the largest axially symmetric convex set S contained in C, and the smallest such set S′ that...
Mobility Improves Coverage of Sensor Networks (2005)
Liu, Benyuan, Brass, Peter, Dousse, Olivier, Nain, Philippe, Towsley, Don
Previous work on the coverage of mobile sensor networks focuses on algorithms to reposition sensors in order to achieve a static configuration with an enlarged covered area. In this paper, we study...
Triangles of extremal area or perimeter in a finite planar point set. (2001)
Brass, Peter, Rote, Gunter, Swanepoel, Konrad
We show the following two results on a set of n points in the plane, thus answering questions posed by Erdos and Purdy [11]: 1. The maximum number of triangles of maximum area (or of maximum...
On the Number of Maximum-Area Triangles in a Planar Pointset (1999)
In this note we prove that in a set of n points in the plane, not all on a line, the maximum area of a triangle is reached by at most n of the n 3 triangles determined by these points, and this...
On Strongly Normal Tesselations (1999)
: A tesselation C is called strongly normal, if it is normal (topological discs with intersections that are either empty or connected) and for any subset of cells C 1 ; : : : ; C k ; C of the...
On Point Sets fixing a Convex Body from within (1997)
: We study the concept of a set fixing a convex body from within that was recently proposed by V. Soltan. We prove his conjecture that a finite set which fixes a d-dimensional convex body from within...
Extremale Konstruktionen in der kombinatorischen Geometrie / (1996)
Greifswald, Universiẗat, Habil.-Schr., 1996.