La geometria computacional, àrea primordial d'actuació del grup, és una disciplina a cavall entre les matemàtiques i la informàtica teòrica. El seu objectiu principal és el disseny i l'anàlisi d'algorismes per a la solució eficient de problemes geomètrics. En conseqüència, una tasca fonamental és la identificació de conceptes, propietats i tècniques que ajudin a la descoberta i implementació d'algorismes eficients. Això comporta l'estudi d'estructures de dades geomètriques, la complexitat d'algorismes, la representació i manipulació de figures i d'objectes, la construcció de llocs geomètrics i, més en general, el desenvolupament de la fonamentació geomètrica. En particular, els problemes estudiats inclouen la cerca i el recompte geomètrics, la convexitat i els processos afins, la proximitat, la intersecció, la triangulació, l'aproximació de formes i la visibilitat. Les àrees principals d'aplicació són la informàtica gràfica, el disseny i la fabricació assistits per ordinador, el reconeixement de formes, la morfologia geomètrica, el disseny VLSI, la visió per computador, els sistemes d'informació geogràfica i la robòtica.

http://futur.upc.edu/DCCG

Computational geometry, which is the main area of activity of the group, is a discipline that lies between mathematics and theoretical computer science. The group?s main objective is the design and analysis of algorithms for efficiently solving geometric problems. As a consequence, a fundamental task is to identify concepts, properties and techniques that will help to find and implement efficient geometric algorithms. This involves the study of geometric data structures, algorithm complexity, the representation and manipulation of figures and objects, geometric loci construction and, in general, the development of geometric principles. The problems studied include geometric search and enumeration, convexity and affine processes, proximity, intersection, triangulation, shape approximation and visibility. The main areas of application are computer graphics, computer-aided design and manufacturing, pattern recognition, computational morphology, VLSI design, computer vision, geographical information systems and robotics.

http://futur.upc.edu/DCCG

Recent Submissions

  • On the Partition Dimension and the Twin Number of a Graph 

    Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel (2016-03-05)
    External research report
    Open Access
    A partition of the vertex set of a connected graph G is a locating partition of G if every vertex is uniquely determined by its vector of distances to the elements of . The partition dimension of G is the minimum ...
  • Perfect and quasiperfect domination in trees 

    Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, Maria Luz (2016-04-25)
    Article
    Open Access
    A k quasip erfect dominating set of a connected graph G is a vertex subset S such that every vertex not in S is adjacent to at least one and at most k vertices in S . The cardinality of a minimum k-quasip erfect dominating ...
  • Opening the black box of energy throughputs in farm systems: a decomposition analysis between the energy returns to external inputs, internal biomass reuses and total inputs consumed (the Vallès County, Catalonia, c.1860 and 1999) 

    Tello, E.; Galán, E.; Sacristán Adinolfi, Vera; Cunfer, G.; Guzmán, G. I.; González de Molina, M.; Krausmann, F.; Gringrich, S.; Padró, R.; Marco, I.; Moreno-Delgado, D. (2016)
    Article
    Restricted access - publisher's policy
    We present an energy analysis of past and present farm systems aimed to contribute to their sustainability assessment. Looking at agroecosystems as a set of energy loops between nature and society, and adopting a farm-operator ...
  • Lower bounds on the maximum number of non-crossing acyclic graphs 

    Huemer, Clemens; Mier Vinué, Anna de (2015-08-01)
    Article
    Restricted access - publisher's policy
    This paper is a contribution to the problem of counting geometric graphs on point sets. More concretely, we look at the maximum numbers of non-crossing spanning trees and forests. We show that the so-called double chain ...
  • On k-gons and k-holes 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 (2015-08-01)
    Article
    Open Access
    We consider a variation of the classical Erdos-Szekeres problems on the existence and number of convex k-gons and k-holes (empty k-gons) in a set of n points in the plane. Allowing the k-gons to be non-convex, we show ...
  • Ramsey numbers for empty convex polygons 

    Bautista-Santiago, Crevel; Cano, Javier; Fabila-Monroy, Ruy; Hidalgo-Toscano, Carlos; Huemer, Clemens; Leaños, Jesús; Sakai, Toshinori; Urrutia, Jorge (University of Ljubljana, 2015)
    Conference report
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    We study a geometric Ramsey type problem where the vertices of the complete graph Kn are placed on a set S of n points in general position in the plane, and edges are drawn as straight-line segments. We define the empty ...
  • On the disks with diameters the sides of a convex 5-gon 

    Huemer, Clemens; Pérez-Lantero, Pablo (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II (MA2), 2015)
    Conference report
    Restricted access - publisher's policy
    We prove that for any convex pentagon there are two disks, among the five disks having a side of the pentagon as diameter and the midpoint of the side as its center, that do not intersect. This shows that K5 is never the ...
  • Blocking the k-holes of point sets in the plane 

    Cano, Javier; Garcia Olaverri, Alfredo Martin; Hurtado Díaz, Fernando Alfredo; Shakai, Toshinori; Tejel Altarriba, Francisco Javier; Urrutia Galicia, Jorge (2015-09)
    Article
    Open Access
    Let P be a set of n points in the plane in general position. A subset H of P consisting of k elements that are the vertices of a convex polygon is called a k-hole of P, if there is no element of P in the interior of its ...
  • The diameter of cyclic Kautz digraphs 

    Böhmová, Katerina; Dalfó Simó, Cristina; Huemer, Clemens (2015-11-12)
    Article
    Restricted access - publisher's policy
    A prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a new family of digraphs with minimal diameter, that is, given ...
  • 3-colorability of pseudo-triangulations 

    Aichholzer, Oswin; Aurenhammer, Franz; Hackl, Thomas; Huemer, Clemens; Pilz, Alexander; Vogtenhuber, Birgit (2015)
    Article
    Restricted access - publisher's policy
    Deciding 3-colorability for general plane graphs is known to be an NP-complete problem. However, for certain families of graphs, like triangulations, polynomial time algorithms exist. We consider the family of pseudo-tri ...

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