Now showing items 1-20 of 43

  • A polynomial bound for untangling geometric planar graphs 

    Bose, Prosenjit; Dujmovic, Vida; Hurtado Díaz, Fernando Alfredo; Langerman, Stefan; Morin, Pat; Wood, David (2009-12)
    Article
    Open Access
    To untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings. Pach and Tardos (Discrete Comput. Geom. 28(4): 585–592, 2002) asked if every n-vertex geometric planar ...
  • Balanced partitions of 3-colored geometric sets in the plane 

    Bereg, Sergey; Hurtado Díaz, Fernando Alfredo; Kano, Mikio; Korman, Matias; Lara, Dolores; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio; Urrutia Galicia, Jorge; Verbeek, Kevin (2015)
    Article
    Open Access
    Let SS be a finite set of geometric objects partitioned into classes or colors . A subset S'¿SS'¿S is said to be balanced if S'S' contains the same amount of elements of SS from each of the colors. We study several ...
  • 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 ...
  • Cell-paths in mono- and bichromatic line arrangements in the plane 

    Aichholzer, Oswin; Cardinal, Jean; Hackl, Thomas; Hurtado Díaz, Fernando Alfredo; Korman Cozzetti, Matías; Pilz, Alexander; Silveira, Rodrigo Ignacio; Uehara, Ryuhei; Vogtenhuber, Birgit; Welzl, Emo (2014)
    Conference report
    Open Access
    We show that in every arrangement of n red and blue lines | in general position and not all of the same color | there is a path through a linear number of cells where red and blue lines are crossed alternatingly (and no ...
  • Colored Ray configurations 

    Fabila Monroy, Ruy; Garcia Olaverri, Alfredo Martin; Hurtado Díaz, Fernando Alfredo; Jaume, Rafel; Pérez Lantero, Pablo; Saumell, Maria; Silveira, Rodrigo Ignacio; Tejel Altarriba, Francisco Javier; Urrutia Galicia, Jorge (2014)
    Conference report
    Open Access
    We study the cyclic sequences induced at in nity by pairwise-disjoint colored rays with apices on a given bal- anced bichromatic point set, where the color of a ray is inherited from the color of its apex. We derive a lower ...
  • Colored ray configurations 

    Fabila Monroy, Ruy; Garcia Olaverri, Alfredo Martin; Hurtado Díaz, Fernando Alfredo; Jaume, Rafel; Pérez Lantero, Pablo; Saumell, Maria; Silveira, Rodrigo Ignacio; Tejel Altarriba, Francisco Javier; Urrutia Galicia, Jorge (2018-05)
    Article
    Open Access
    We study the cyclic color sequences induced at infinity by colored rays with apices being a given balanced finite bichromatic point set. We first study the case in which the rays are required to be pairwise disjoint. We ...
  • Colored spanning graphs for set visualization 

    Hurtado Díaz, Fernando Alfredo; Korman Cozzetti, Matías; Van Kreveld, Matias; Löffler, Maarten; Sacristán Adinolfi, Vera; Silveira, Rodrigo Ignacio; Speckmann, Bettina (Springer, 2013)
    Conference report
    Open Access
    We study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the ...
  • Colored spanning graphs for set visualization 

    Hurtado Díaz, Fernando Alfredo; Korman, Matias; Van Kreveld, Matias; Löffler, Maarten; Sacristán Adinolfi, Vera; Shioura, Akiyoshi; Silveira, Rodrigo Ignacio; Speckmann, Bettina; Tokuyama, Takeshi (2018-03)
    Article
    Open Access
    We study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the ...
  • Compatible matchings in geometric graphs 

    Aichholzer, Oswin; García Olaverri, Alfredo; Hurtado Díaz, Fernando Alfredo; Tejel Altarriba, F. Javier (Centre de Recerca Matemàtica, 2011)
    Conference report
    Open Access
    Two non-crossing geometric graphs on the same set of points are compatible if their union is also non-crossing. In this paper, we prove that every graph G that has an outerplanar embedding admits a non-crossing perfect ...
  • Compatible spanning trees 

    Garcia Olaverri, Alfredo Martin; Huemer, Clemens; Hurtado Díaz, Fernando Alfredo; Tejel Altarriba, Francisco Javier (2014-07-01)
    Article
    Open Access
    Two plane geometric graphs are said to be compatible when their union is a plane geometric graph. Let S be a set of n points in the Euclidean plane in general position and let T be any given plane geometric spanning tree ...
  • Configurations of non-crossing rays and related problems 

    Garcia Olaverri, Alfredo Martin; Hurtado Díaz, Fernando Alfredo; Tejel Altarriba, Francisco Javier; Urrutia Galicia, Jorge (2016-04)
    Article
    Open Access
    Let S be a set of n points in the plane and let R be a set of n pairwise non-crossing rays, each with an apex at a different point of S. Two sets of non-crossing rays R1R1 and R2R2 are considered to be different if the ...
  • Connectivity-preserving transformations of binary images 

    Bose, Prosenjit; Dujmovic, Vida; Hurtado Díaz, Fernando Alfredo; Morin, Pat (2009-10)
    Article
    Open Access
    A binary image $\emph{I}$ is $B_a$, $W_b$-connected, where $\emph{a,b}$ ∊ {4,8}, if its foreground is $\emph{a}$-connected and its background is $\emph{b}$-connected. We consider a local modification of a $B_a$, $W_b$-connected ...
  • Coverage with k-transmitters in the presence of obstacles 

    Uehara, R.; Souvaine, D.; Sacristán Adinolfi, Vera; Morin, P.; Lubiw, A.; Iacono, J.; Ballinger, B.; Benbernou, N.; Bose, P.; Damian, M.; Demaine, E. D.; Dujmovic, Vida; Flatland, R.; Hurtado Díaz, Fernando Alfredo (Springer Verlag, 2010)
    Conference report
    Restricted access - publisher's policy
    For a fixed integer k ≥ 0, a k-transmitter is an omnidirectional wireless transmitter with an infinite broadcast range that is able to penetrate up to k “walls”, represented as line segments in the plane. We develop lower ...
  • Distance 2-domination in prisms of graphs 

    Hurtado Díaz, Fernando Alfredo; Mora Giné, Mercè; Rivera Campo, Eduardo; Zuazua Vega, Rita Esther (2017-01-01)
    Article
    Open Access
    A set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ¿ ( V ( G ) - D ) and D is at most two. Let ¿ 2 ( G ) denote the size of a smallest distance 2 -dominating set of ...
  • Edge-Removal and Non-Crossing Configurations in Geometric Graphs 

    Aichholzer, Oswin; Cabello, Sergio; Fabila Monroy, Ruy; Flores Peñaloza, David; Hackl, Thomas; Huemer, Clemens; Hurtado Díaz, Fernando Alfredo; Wood, David (2010)
    Article
    Open Access
    A geometric graph is a graph G = (V;E) drawn in the plane, such that V is a point set in general position and E is a set of straight-line segments whose endpoints belong to V . We study the following extremal problem for ...
  • Every large point set contains many collinear points or an empty pentagon 

    Wood, David; Por, Attila; Abel, Zachary; Ballinger, Brad; Bose, Prosenjit; Collette, Sébastien; Dujmovic, Vida; Hurtado Díaz, Fernando Alfredo; Kominers, Scott Duke; Langerman, Stefan (2011-01)
    Article
    Restricted access - publisher's policy
    We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next ...
  • Geometric biplane graphs II: graph augmentation 

    Garcia Olaverri, Alfredo Martin; Hurtado Díaz, Fernando Alfredo; Korman Cozzetti, Matías; Matos, Inés P.; Saumell, Maria; Silveira, Rodrigo Ignacio; Tejel Altarriba, Francisco Javier; Tóth, Csaba D. (2015-03-01)
    Article
    Open Access
    We study biplane graphs drawn on a finite point set in the plane in general position. This is the family of geometric graphs whose vertex set is and which can be decomposed into two plane graphs. We show that every ...
  • Geometric Biplane Graphs II: Graph Augmentation 

    Hurtado Díaz, Fernando Alfredo; Garcia Olaverri, Alfredo Martin; Korman Cozzetti, Matías; Matos, Inés P.; Saumell, Maria; Silveira, Rodrigo Ignacio; Tejel Altarriba, Francisco Javier; Tóth, Csaba D. (2013)
    Conference report
    Open Access
    We study biplane graphs drawn on a nite point set S in the plane in general position. This is the family of geometric graphs whose vertex set is S and which can be decomposed into two plane graphs. We show that every ...
  • Geometric biplane graphs I: maximal graphs 

    Hurtado Díaz, Fernando Alfredo; Garcia Olaverri, Alfredo Martin; Korman Cozzetti, Matías; Matos, Inés P.; Saumell, Maria; Silveira, Rodrigo Ignacio; Tejel Altarriba, Francisco Javier; Tóth, Csaba D. (2013)
    Conference report
    Open Access
  • Geometric biplane graphs I: maximal graphs 

    Garcia Olaverri, Alfredo Martin; Hurtado Díaz, Fernando Alfredo; Korman Cozzetti, Matías; Matos, Inés P.; Saumell, Maria; Silveira, Rodrigo Ignacio; Tejel Altarriba, Francisco Javier; Tóth, Csaba D. (2015-03-01)
    Article
    Open Access
    We study biplane graphs drawn on a finite planar point set in general position. This is the family of geometric graphs whose vertex set is and can be decomposed into two plane graphs. We show that two maximal biplane ...