For a sufficiently dense set of points in any closed Riemannian manifold, we prove that a unique Delannay triangulation exists. This triangulation has the same properties as in Eu...
Though Delaunay triangulations are very well known geometric data structures, the problem of the robust removal of a vertex in a three-dimensional Delaunay triangulation is still ...
Let S be a finite set of points in the Euclidean plane, and let E be the complete graph whose point-set is S. Chew, in 1986, proved a lower bound of /2 on the stretch factor of th...
We consider online routing algorithms for routing between the vertices of embedded planar straight line graphs. Our results include (1) two deterministic memoryless routing algorit...
Abstract. We show that there is a matching between the edges of any two triangulations of a planar point set such that an edge of one triangulation is matched either to the identic...
Oswin Aichholzer, Franz Aurenhammer, Michael Tasch...