Now showing items 1-16 of 16

    • 4-Holes in point sets 

      Aichholzer, Oswin; Fabila Monroy, Ruy; Gonzalez Aguilar, Hernan; Hackl, Thomas; Heredia, Marco A.; Huemer, Clemens; Urrutia Galicia, Jorge; Vogtenhuber, Birgit (2014-08-01)
      Article
      Open Access
      We consider a variant of a question of Erdos on the number of empty k-gons (k-holes) in a set of n points in the plane, where we allow the k-gons to be non-convex. We show bounds and structural results on maximizing and ...
    • 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 ...
    • 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
      Open Access
      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 ...
    • 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 ...
    • 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 ...
    • 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
      Open Access
      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 ...
    • Empty monochromatic simplices 

      Aichholzer, Oswin; Fabila Monroy, Ruy; Hackl, Thomas; Huemer, Clemens; Urrutia Galicia, Jorge (2014-03-01)
      Article
      Open Access
      Let S be a k-colored (finite) set of n points in , da parts per thousand yen3, in general position, that is, no (d+1) points of S lie in a common (d-1)-dimensional hyperplane. We count the number of empty monochromatic ...
    • Modem illumination of monotone polygons 

      Aichholzer, Oswin; Fabila Monroy, Ruy; Flores Peñaloza, David; Hackl, Thomas; Huemer, Clemens; Urrutia Galicia, Jorge; Vogtenhuber, Birgit (2009)
      Conference report
      Open Access
      We study a generalization of the classical problem of illumination of polygons. Instead of modeling a light source we model a wireless device whose radio signal can penetrate a given number k of walls. We call these ...
    • On k-gons and k-holes in point sets 

      Aichholzer, Oswin; Fabila Monroy, Ruy; Gonzalez Aguilar, Hernan; Hackl, Thomas; Heredia, Marco A.; Huemer, Clemens; Urrutia Galicia, Jorge; Valtr, Pavel; Vogtenhuber, Birgit (2015-08-01)
      Article
      Open Access
      We consider a variation of the classical Erdos-Szekeres problems on the existence and number of convex k-gons and k-holes (empty k-gons) in a set of n points in the plane. Allowing the k-gons to be non-convex, we show ...
    • On the Oß-hull of a planar point set 

      Alegría Galicia, Carlos; Orden, David; Seara Ojea, Carlos; Urrutia Galicia, Jorge (2018-03-01)
      Article
      Open Access
      We study the Oß-hull of a planar point set, a generalization of the Orthogonal Convex Hull where the coordinate axes form an angle ß. Given a set P of n points in the plane, we show how to maintain the Oß-hull of P while ...
    • Order types and cross-sections of line arrangements in R^3 

      Aichholzer, Oswin; Fabila-Monroy, Ruy; Hurtado Díaz, Fernando Alfredo; Pérez Lantero, Pablo; Ruiz Vargas, Andrés; Urrutia Galicia, Jorge; Vogtenhuber, Birgit (2014)
      Conference report
      Restricted access - publisher's policy
      We consider sets L = {l1,...., ln} of n labeled lines in general position in R3, and study the order types of point sets fp1; : : : ; png that stem from the intersections of the lines in L with (directed) planes II, not ...
    • Rectilinear convex hull of points in 3D and applications 

      Pérez Lantero, Pablo; Seara Ojea, Carlos; Urrutia Galicia, Jorge (Springer, 2024-05-04)
      Article
      Open Access
      Let P be a set of n points in R3 in general position, and let RCH(P) be the rectilinear convex hull of P. In this paper we obtain an optimal O(n log n) time and O(n) space algorithm to compute RCH(P). We also obtain an ...
    • Separating bichromatic point sets in the plane by restricted orientation convex hulls 

      Alegría Galicia, Carlos; Orden Martin, David; Seara Ojea, Carlos; Urrutia Galicia, Jorge (2023-04-01)
      Article
      Open Access
      We explore the separability of point sets in the plane by a restricted-orientation convex hull, which is an orientation-dependent, possibly disconnected, and non-convex enclosing shape that generalizes the convex hull. Let ...
    • Stabbing simplices of point sets with k-flats 

      Cano, Javier; Hurtado Díaz, Fernando Alfredo; Urrutia Galicia, Jorge (Universidad de Sevilla, 2013)
      Conference report
      Open Access
      Let S be a set of n points inRdin general position.A set H of k-flats is called an mk-stabber of S if the relative interior of anym-simplex with vertices in S is intersected by at least one element of H. In thispaper we ...