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

  • Computing optimal shortcuts for networks 

    Garijo Royo, Delia; Marquez Pérez, Alberto; Rodríguez, Natalia; Silveira, Rodrigo Ignacio (Elsevier, 2019-11-16)
    Article
    Restricted access - publisher's policy
    We study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received ...
  • Capturing points with a rotating polygon (and a 3D extension) 

    Alegría Galicia, Carlos; Orden, David; Palios, Leonidas; Seara Ojea, Carlos; Urrutia Galicia, Jorge (2019-04)
    Article
    Restricted access - publisher's policy
    We study the problem of rotating a simple polygon to contain the maximum number of elements from a given point set in the plane. We consider variations of this problem where the rotation center is a given point or lies on ...
  • Region-based approximation of probability distributions (for visibility between imprecise points among obstacles) 

    Buchin, Kevin; Kostitsyna, Irina; Löffler, Maarten; Silveira, Rodrigo Ignacio (2019-07)
    Article
    Open Access
    Let p and q be two imprecise points, given as probability density functions on R2 , and let O be a set of disjoint polygonal obstacles in R2 . We study the problem of approximating the probability that p and q can see each ...
  • Metric dimension of maximal outerplanar graphs 

    Claverol Aguas, Mercè; Hernando Martín, María del Carmen; Maureso Sánchez, Montserrat; Mora Giné, Mercè; Hernández Peñalver, Gregorio; Garcia Olaverri, Alfredo Martin; Tejel, Javier (2019-03-28)
    External research report
    Open Access
  • Trees whose even-degree vertices induce a path are antimagic 

    Lozano Bojados, Antoni; Mora Giné, Mercè; Seara Ojea, Carlos; Tey Carrera, Joaquín (2019-05-16)
    External research report
    Open Access
    An antimagic labeling of a connected 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 v is the sum of the labels ...
  • Compatible Paths on Labelled Point Sets 

    Arseneva, Elena; Bahoo, Yeganeh; Biniaz, Ahmad; Cano Vila, María del Pilar; Chanchary, Farah; Iacono, John; Jain, Kshitij; Lubiw, Anna; Mondal, Debajyoti; Sheikhan, Khadijeh; D. Thót, Csaba (2019)
    Conference report
    Open Access
    Let 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 

    Arseneva, Elena; Bose, Prosenjit; Cano Vila, María del Pilar; D'Angelo, Anthony; Dujmovic, Vida; Frati, Fabrizio; Langerman, Stefan; Tappini, Alessandra
    Conference report
    Restricted access - publisher's policy
    We study the question whether a crossing-free 3D morph between two straight-line drawings of an n-vertex 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 L-infinity Delaunay triangulations 

    Bose, Prosenjit; Cano Vila, María del Pilar; Silveira, Rodrigo Ignacio (2018)
    Conference report
    Open Access
    We extend a known result about L2-Delaunay triangulations to L∞-Delaunay. Let TS be the set of all non-crossing spanning trees of a planar n-point set S. We prove that for each element T of TS, there exists a length-decreasing ...
  • Computing optimal shortcuts for networks 

    Garijo Royo, Delia; Marquez Pérez, Alberto; Rodríguez, Natalia; Silveira, Rodrigo Ignacio (2018)
    Conference report
    Open Access
    We 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 

    Garijo Royo, Delia; Marquez Pérez, Alberto; Rodríguez, Natalia; Silveira, Rodrigo Ignacio (2018)
    Conference report
    Open Access
    We 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 ...
  • Antimagic labelings of caterpillars 

    Lozano Bojados, Antoni; Mora Giné, Mercè; Seara Ojea, Carlos (2019-04-15)
    Article
    Restricted access - publisher's policy
    A k-antimagic labeling of a graph G is an injection from E(G) to {1,2, ..., |E(G)|+k} such that all vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of the labels assigned to edges incident ...
  • A note on flips in diagonal rectangulations 

    Cardinal, Jean; Sacristán Adinolfi, Vera; Silveira, Rodrigo Ignacio (Chapman & Hall/CRC, 2018-11-09)
    Article
    Open Access
    Rectangulations are partitions of a square into axis-aligned rectangles. A number of results provide bijections between combinatorial equivalence classes of rectangulations and families of pattern-avoiding permutations. ...

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