Browsing by Author "Urrutia Galicia, Jorge"
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4Holes in point sets
Aichholzer, Oswin; Fabila Monroy, Ruy; Gonzalez Aguilar, Hernan; Hackl, Thomas; Heredia, Marco A.; Huemer, Clemens; Urrutia Galicia, Jorge; Vogtenhuber, Birgit (20140801)
Article
Open AccessWe consider a variant of a question of Erdos on the number of empty kgons (kholes) in a set of n points in the plane, where we allow the kgons to be nonconvex. We show bounds and structural results on maximizing and ... 
Balanced partitions of 3colored 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 AccessLet 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 kholes 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 (201509)
Article
Open AccessLet 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 khole 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 (201904)
Article
Open AccessWe 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 AccessWe study the cyclic sequences induced at in nity by pairwisedisjoint 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 (201805)
Article
Open AccessWe 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 noncrossing rays and related problems
Garcia Olaverri, Alfredo Martin; Hurtado Díaz, Fernando Alfredo; Tejel Altarriba, Francisco Javier; Urrutia Galicia, Jorge (201604)
Article
Open AccessLet S be a set of n points in the plane and let R be a set of n pairwise noncrossing rays, each with an apex at a different point of S. Two sets of noncrossing rays R1R1 and R2R2 are considered to be different if the ... 
Efficient computation of minimumarea rectilinear convex hull under rotation and generalizations
Alegría Galicia, Carlos; Orden Martin, David; Seara Ojea, Carlos; Urrutia Galicia, Jorge (Springer Nature, 202103)
Article
Open AccessLet 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 (20140301)
Article
Open AccessLet S be a kcolored (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 (d1)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 AccessWe 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 kgons and kholes 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 (20150801)
Article
Open AccessWe consider a variation of the classical ErdosSzekeres problems on the existence and number of convex kgons and kholes (empty kgons) in a set of n points in the plane. Allowing the kgons to be nonconvex, we show ... 
On the Oßhull of a planar point set
Alegría Galicia, Carlos; Orden, David; Seara Ojea, Carlos; Urrutia Galicia, Jorge (20180301)
Article
Open AccessWe study the Oßhull 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 Oßhull of P while ... 
Order types and crosssections of line arrangements in R^3
Aichholzer, Oswin; FabilaMonroy, Ruy; Hurtado Díaz, Fernando Alfredo; Pérez Lantero, Pablo; Ruiz Vargas, Andrés; Urrutia Galicia, Jorge; Vogtenhuber, Birgit (2014)
Conference report
Restricted access  publisher's policyWe 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, 20240504)
Article
Open AccessLet 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 (20230401)
Article
Open AccessWe explore the separability of point sets in the plane by a restrictedorientation convex hull, which is an orientationdependent, possibly disconnected, and nonconvex enclosing shape that generalizes the convex hull. Let ... 
Stabbing simplices of point sets with kflats
Cano, Javier; Hurtado Díaz, Fernando Alfredo; Urrutia Galicia, Jorge (Universidad de Sevilla, 2013)
Conference report
Open AccessLet S be a set of n points inRdin general position.A set H of kflats is called an mkstabber of S if the relative interior of anymsimplex with vertices in S is intersected by at least one element of H. In thispaper we ...