Recent Submissions

  • 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 ...
  • A new lower bound on the maximum number of plane graphs using production matrices 

    Huemer, Clemens; Pilz, Alexander; Silveira, Rodrigo Ignacio (2018)
    Conference lecture
    Restricted access - publisher's policy
    We use the concept of production matrices to show that there exist sets of n points in the plane that admit ¿(41.77n) crossing-free geometric graphs. This improves the previously best known bound of ¿(41.18n) by Aichholzer ...
  • Non-crossing paths with geographic constraints 

    Silveira, Rodrigo Ignacio; Speckmann, Bettina; Verbeek, Kevin (Springer, 2018)
    Conference report
    Restricted access - publisher's policy
    A geographic network is a graph whose vertices are restricted to lie in a prescribed region in the plane. In this paper we begin to study the following fundamental problem for geographic networks: can a given geographic ...
  • Geomasking through perturbation, or counting points in circles 

    Löffler, Maarten; Luo, Jun; Silveira, Rodrigo Ignacio (2017)
    Conference report
    Restricted access - publisher's policy
    Motivated by a technique in privacy protection, in which n points are randomly perturbed by at most a distance r, we study the following problem: Given n points and m circles in the plane, what is the maximum r such that ...

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