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Farthest color Voronoi diagrams: complexity and algorithms
(Springer, 2021)
Conference report
Restricted access  publisher's policyThe farthestcolor Voronoi diagram (FCVD) is a farthestsite Voronoi structure defined on a family P of m pointclusters in the plane, where the total number of points is n. The FCVD finds applications in problems related ... 
Flips in higher order Delaunay triangulations
(2021)
Conference report
Restricted access  publisher's policyWe study the flip graph of higher order Delaunay triangulations. A triangulation of a set S of n points in the plane is orderk Delaunay if for every triangle its circumcircle encloses at most k points of S. The flip graph ... 
Affine invariant triangulations
(2019)
Conference report
Restricted access  publisher's policyWe study affine invariant 2D triangulation methods. That is, methods that produce the same triangulation for a point set S for any (unknown) affine transformation of S. Our work is based on a method by Nielson [A ... 
Hamiltonicity for convex shape Delaunay and Gabriel Graphs
(Springer, 2019)
Conference report
Restricted access  publisher's policyWe study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Instead of defining these proximity graphs using circles, we use an arbitrary convex shape C. Let S be a point set in the plane. ... 
Hamiltonicity for convex shape Delaunay and Gabriel graphs
(2019)
Conference report
Restricted access  publisher's policyWe study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Let S be a point set in the plane. The korder Delaunay graph of S, denoted kDGC(S), has vertex set S and edge pq provided ... 
Compatible Paths on Labelled Point Sets
(2019)
Conference report
Open AccessLet P and Q be finite point sets of the same cardinality in R 2 , each labelled from 1 to n. Two noncrossing geometric graphs GP and GQ spanning P and Q, respectively, are called compatible if for every face f in GP , there ... 
Pole Dancing: 3D Morphs for Tree Drawings
(Springer, 2018)
Conference report
Restricted access  publisher's policyWe study the question whether a crossingfree 3D morph between two straightline drawings of an nvertex tree can be constructed consisting of a small number of linear morphing steps. We look both at the case in which the ... 
Sequences of spanning trees for Linfinity Delaunay triangulations
(2018)
Conference report
Open AccessWe extend a known result about L2Delaunay triangulations to L∞Delaunay. Let TS be the set of all noncrossing spanning trees of a planar npoint set S. We prove that for each element T of TS, there exists a lengthdecreasing ... 
Computing optimal shortcuts for networks
(2018)
Conference report
Open AccessWe augment a plane Euclidean network with a segment or shortcut to minimize the largest distance between any two points along the edges of the resulting network. In this continuous setting, the problem of computing distances ... 
Computing optimal shortcuts for networks
(2018)
Conference report
Open AccessWe study augmenting a plane Euclidean network with a segment, called shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Questions of this type have received considerable ... 
A new lower bound on the maximum number of plane graphs using production matrices
(2018)
Conference lecture
Restricted access  publisher's policyWe use the concept of production matrices to show that there exist sets of n points in the plane that admit ¿(41.77n) crossingfree geometric graphs. This improves the previously best known bound of ¿(41.18n) by Aichholzer ... 
Noncrossing paths with geographic constraints
(Springer, 2018)
Conference report
Restricted access  publisher's policyA geographic network is a graph whose vertices are restricted to lie in a prescribed region in the plane. In this paper we begin to study the following fundamental problem for geographic networks: can a given geographic ...