Now showing items 1-12 of 12

• #### Hamiltonicity for convex shape Delaunay and Gabriel graphs ﻿

(2019)
Conference report
Restricted access - publisher's policy
We study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Let S be a point set in the plane. The k-order Delaunay graph of S, denoted k-DGC(S), has vertex set S and edge pq provided ...
• #### Hamiltonicity for convex shape Delaunay and Gabriel graphs ﻿

(2020-08)
Article
Open Access
We 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 $$\mathcal {C}$$ . Let S be a point ...
• #### Hamiltonicity for convex shape Delaunay and Gabriel Graphs ﻿

(Springer, 2019)
Conference report
Restricted access - publisher's policy
We 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. ...
• #### Improving shortest paths in the Delaunay triangulation ﻿

(2012)
Article
Open Access
We study a problem about shortest paths in Delaunay triangulations. Given two nodes s, t in the Delaunay triangulation of a point set P, we look for a new point p that can be added, such that the shortest path from s to ...
• #### Matching points with things ﻿

(Springer Verlag, 2010)
Conference report
Restricted access - publisher's policy
Given an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a non-crossing matching between point-object pairs. We show that when the objects we match the points to ...
• #### Mesures de regularitat per a polígons convexos ﻿

(Universitat Politècnica de Catalunya, 2008)
Master thesis
Open Access
Al llarg d'aquesta memòria, hem plantejat possibles mesures de regularitat, totes elles justificades, per a un n-gon convex qualsevol que han donat lloc a problemes de geometria discreta i computacional. A més, hem estat ...
• #### On the number of higher order Delaunay triangulations ﻿

(Springer Verlag, 2010)
Conference report
Restricted access - publisher's policy
Higher order Delaunay triangulations are a generalization of the Delaunay triangulation which provides a class of well-shaped triangulations, over which extra criteria can be optimized. A triangulation is order-k Delaunay ...
• #### Proximity graphs inside large weighted graphs ﻿

(2010)
Conference report
Open Access
Given a large weighted graph G = (V;E) and a subset U of V , we de¯ne several graphs with vertex set U in which two vertices are adjacent if they satisfy some prescribed proximity rule. These rules use the shortest path ...
• #### Recoloring directed graphs ﻿

(Prensas Universitarias de Zaragoza, 2009)
Conference report
Open Access
Let G be a directed graph and k a positive integer. We define the k-color graph of G (Dk(G) for short) as the directed graph having all k-colorings of G as node set, and where two k-colorings and ' are joined by a ...
• #### Some properties of higher order delaunay and gabriel graphs ﻿

(2010)
Conference report
Open Access
We consider two classes of higher order proximity graphs defined on a set of points in the plane, namely, the k-Delaunay graph and the k-Gabriel graph. We give bounds on the following combinatorial and geometric properties ...
• #### Terrain prickliness: theoretical grounds for high complexity viewsheds ﻿

(2021)
Conference report
Open Access
An important task when working with terrain models is computing viewsheds: the parts of the terrain visible from a given viewpoint. When the terrain is modeled as a polyhedral terrain, the viewshed is composed of the union ...
• #### Terrain prickliness: theoretical grounds for low complexity viewsheds ﻿

(2021)
Conference report
Restricted access - publisher's policy