Recent Submissions

  • 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 ...
  • 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 (Springer, 2018)
    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 ...