Browsing by Author "Aichholzer, Oswin"

Geodesic order types
Aichholzer, Oswin; Korman Cozzetti, Matías; Pilz, Alexander; Vogtenhuber, Birgit (20140901)
Article
Restricted access  publisher's policyThe geodesic between two points a and b in the interior of a simple polygon P is the shortest polygonal path inside P that connects a to b. It is thus the natural generalization of straight line segments on unconstrained ... 
Large bichromatic point sets admit empty monochromatic 4gons
Aichholzer, Oswin; Hackl, Thomas; Huemer, Clemens; Hurtado Díaz, Fernando Alfredo; Vogtenhuber, Birgit (2009)
Conference report
Open AccessWe consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that ... 
Lower bounds for the number of small convex kholes
Aichholzer, Oswin; Fabila Monroy, Ruy; Hackl, Thomas; Huemer, Clemens; Pilz, Alexander; Vogtenhuber, Birgit (20140701)
Article
Open AccessLet S be a set of n points in the plane in general position, that is, no three points of S are on a line. We consider an Erdostype question on the least number h(k)(n) of convex kholes in S, and give improved lower bounds ... 
Maximizing maximal angles for plane straightline graphs
Aichholzer, Oswin; Hackl, Thomas; Hoffmann, Michael; Huemer, Clemens; Pór, Attila; Santos, Francisco; Speckmann, Bettina; Vogtenhuber, Birgit (201301)
Article
Restricted access  publisher's policyLet G=(S,E) be a plane straightline graph on a finite point set S⊂R2 in general position. The incident angles of a point p∈S in G are the angles between any two edges of G that appear consecutively in the circular order ... 
Modem illumination of monotone polygons
Aichholzer, Oswin; Fabila Monroy, Ruy; Flores Peñaloza, David; Hackl, Thomas; Huemer, Clemens; Urrutia Galicia, Jorge; Vogtenhuber, Birgit (2009)
Conference report
Open AccessWe 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 walls. We call these ... 
On kgons and kholes in point sets
Aichholzer, Oswin; Fabila Monroy, Ruy; Gonzalez Aguilar, Hernan; Hackl, Thomas; Heredia, Marco A.; Huemer, Clemens; Urrutia Galicia, Jorge; Valtr, Pavel; Vogtenhuber, Birgit (20150801)
Article
Open AccessWe consider a variation of the classical ErdosSzekeres problems on the existence and number of convex kgons and kholes (empty kgons) in a set of n points in the plane. Allowing the kgons to be nonconvex, we show ... 
Order types and crosssections of line arrangements in R^3
Aichholzer, Oswin; FabilaMonroy, Ruy; Hurtado Díaz, Fernando Alfredo; Pérez Lantero, Pablo; Ruiz Vargas, Andrés; Urrutia Galicia, Jorge; Vogtenhuber, Birgit (2014)
Conference report
Restricted access  publisher's policyWe consider sets L = {l1,...., ln} of n labeled lines in general position in R3, and study the order types of point sets fp1; : : : ; png that stem from the intersections of the lines in L with (directed) planes II, not ... 
Twoconvex polygons
Aichholzer, Oswin; Aurenhammer, Franz; Hurtado Díaz, Fernando Alfredo; Ramos, Pedro A.; Urrutia, J. (Université Libre de Bruxelles, 2009)
Conference report
Open AccessWe introduce a notion of kconvexity and explore some properties of polygons that have this property. In particular, 2convex polygons can be recognized in O(n log n) time, and kconvex polygons can be triangulated in O(kn) time.