The research group on Computational Geometry and Applications (CGA) is devoted to carrying out research on computational geometry with a strong emphasis in applications. Computational geometry is an active field in the interface between applied mathematics and computer science that studies algorithmic problems involving discrete geometric objects. The field has applications in robotics, computer graphics, CAD/CAM, integrated circuit design, computer vision, and geographic information science.

The CGA group has the goal of working not only on the design of efficient algorithms, but also on their application to different domains. In particular, we will concentrate on making progress on core geometric problems, and on their applications to two concrete domains: robotics and geographic information science.

Recent Submissions

  • Total domination in plane triangulations 

    Claverol Aguas, Mercè; Garcia Olaverri, Alfredo Martin; Hernández Peñalver, Gregorio; Hernando Martín, María del Carmen; Maureso Sánchez, Montserrat; Mora Giné, Mercè; Tejel Altarriba, Francisco Javier (2021-01-01)
    Article
    Open Access
    A total dominating set of a graph is a subset of such that every vertex in is adjacent to at least one vertex in . The total domination number of , denoted by , is the minimum cardinality of a total dominating set of . A ...
  • A scalable method to construct compact road networks from GPS trajectories 

    Guo, Yuejun; Bardera Reig, Anton; Fort Masdevall, Marta; Silveira, Rodrigo Ignacio (2020-10-06)
    Article
    Restricted access - publisher's policy
    The automatic generation of road networks from GPS tracks is a challenging problem that has been receiving considerable attention in the last years. Although dozens of methods have been proposed, current techniques suffer ...
  • Farthest color Voronoi diagrams: complexity and algorithms 

    Mantas, Ioannis; Papadopoulou, Evanthia; Sacristán Adinolfi, Vera; Silveira, Rodrigo Ignacio (Springer, 2021)
    Conference report
    Restricted access - publisher's policy
    The farthest-color Voronoi diagram (FCVD) is a farthestsite Voronoi structure defined on a family P of m point-clusters in the plane, where the total number of points is n. The FCVD finds applications in problems related ...
  • Efficient computation of minimum-area rectilinear convex hull under rotation and generalizations 

    Alegría Galicia, Carlos; Orden Martin, David; Seara Ojea, Carlos; Urrutia Galicia, Jorge (Springer Nature, 2021-03)
    Article
    Restricted access - publisher's policy
    Let P be a set of n points in the plane. We compute the value of ¿¿[0,2p) for which the rectilinear convex hull of P, denoted by RHP(¿), has minimum (or maximum) area in optimal O(nlogn) time and O(n) space, improving the ...
  • Caterpillars are antimagic 

    Lozano Bojados, Antoni; Mora Giné, Mercè; Seara Ojea, Carlos; Tey Carrera, Joaquín (2021-01-21)
    Article
    Restricted access - publisher's policy
    An antimagic labeling of a graph G is a bijection from the set of edges E(G) to {1,2,…,|E(G)|}, such that all vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of the labels assigned to the ...
  • Flips in higher order Delaunay triangulations 

    Arseneva, Elena; Bose, Prosenjit; Cano Vila, María del Pilar; Silveira, Rodrigo Ignacio (2021)
    Conference report
    Restricted access - publisher's policy
    We study the flip graph of higher order Delaunay triangulations. A triangulation of a set S of n points in the plane is order-k Delaunay if for every triangle its circumcircle encloses at most k points of S. The flip graph ...
  • Affine invariant triangulations 

    Bose, Prosenjit; Cano Vila, María del Pilar; Silveira, Rodrigo Ignacio (2019)
    Conference report
    Restricted access - publisher's policy
    We 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 

    Bose, Prosenjit; Cano Vila, María del Pilar; Saumell Mendiola, Maria; Silveira, Rodrigo Ignacio (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. ...
  • Hamiltonicity for convex shape Delaunay and Gabriel graphs 

    Bose, Prosenjit; Cano Vila, María del Pilar; Saumell Mendiola, Maria; Silveira, Rodrigo Ignacio (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 ...
  • Map construction algorithms: a local evaluation through hiking data 

    Duran, David; Sacristán Adinolfi, Vera; Silveira, Rodrigo Ignacio (2020-02-26)
    Article
    Open Access
    We study five existing map construction algorithms, designed and tested with urban vehicle data in mind, and apply them to hiking trajectories with different terrain characteristics. Our main goal is to better understand ...
  • Hamiltonicity for convex shape Delaunay and Gabriel graphs 

    Bose, Prosenjit; Cano Vila, María del Pilar; Saumell Mendiola, Maria; Silveira, Rodrigo Ignacio (2020-08)
    Article
    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 \(\mathcal {C}\) . Let S be a point ...
  • Convex quadrangulations of bichromatic point sets 

    Pilz, Alexander; Seara Ojea, Carlos (2020-06-05)
    Article
    Open Access
    We consider quadrangulations of red and blue points in the plane where each face is convex and no edge connects two points of the same color. In particular, we show that the following problem is NP-hard: Given a finite set ...

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