From computational geometry comes the notion of a Gabriel graph of a point set in the plane. The Gabriel graph consists of those edges connecting two points of the point set such t...
Θk-graphs are geometric graphs that appear in the context of graph navigation. The shortest-path metric of these graphs is known to approximate the Euclidean complete graph up to...
Nicolas Bonichon, Cyril Gavoille, Nicolas Hanusse,...
New tight bounds are presented on the minimum length of planar straight line graphs connecting n given points in the plane and having convex faces. Specifically, we show that the ...
Let X be a set of points in general position in the plane. General position means that no three points lie on a line and no two points have the same x-coordinate. Y X is a cup, r...
Abstract. In this paper we introduce a new technique for approximation schemes for geometrical optimization problems. As an example problem, we consider the following variant of th...