Browsing by Author "Hurtado Díaz, Fernando Alfredo"

A polynomial bound for untangling geometric planar graphs
Bose, Prosenjit; Dujmovic, Vida; Hurtado Díaz, Fernando Alfredo; Langerman, Stefan; Morin, Pat; Wood, David (200912)
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Open AccessTo 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 nvertex geometric planar ... 
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)
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Restricted access  publisher's policyLet 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)
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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 ... 
Cellpaths 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 AccessWe 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 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 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 AccessWe 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 AccessTwo noncrossing geometric graphs on the same set of points are compatible if their union is also noncrossing. In this paper, we prove that every graph G that has an outerplanar embedding admits a noncrossing perfect ... 
Compatible spanning trees
Garcia Olaverri, Alfredo Martin; Huemer, Clemens; Hurtado Díaz, Fernando Alfredo; Tejel Altarriba, Francisco Javier (20140701)
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Open AccessTwo 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 ... 
Connectivitypreserving transformations of binary images
Bose, Prosenjit; Dujmovic, Vida; Hurtado Díaz, Fernando Alfredo; Morin, Pat (200910)
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Open AccessA 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 ktransmitters 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 policyFor a fixed integer k ≥ 0, a ktransmitter 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 ... 
EdgeRemoval and NonCrossing 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)
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Open AccessA 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 straightline 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 (201101)
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Restricted access  publisher's policyWe 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 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. (20150301)
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Restricted access  publisher's policyWe 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 ... 
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 AccessWe 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 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. (20150301)
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Restricted access  publisher's policyWe 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 tree graphs of points in convex position
Hernando Martín, María del Carmen; Hurtado Díaz, Fernando Alfredo; Márquez Pérez, Alberto; Mora Giné, Mercè; Noy Serrano, Marcos (1997)
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Open AccessGiven a set $P$ of points in the plane, the geometric tree graph of $P$ is defined as the graph $T(P)$ whose vertices are noncrossing rectilinear spanning trees of $P$, and where two trees $T_1$ and $T_2$ are adjacent ... 
Graphs of noncrossing perfect matchings
Hernando Martín, María del Carmen; Hurtado Díaz, Fernando Alfredo; Noy Serrano, Marcos (2001)
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Open AccessLet Pn be a set of n = 2m points that are the vertices of a convex polygon, and let Mm be the graph having as vertices all the perfect matchings in the point set Pn whose edges are straight line segments and do not cross, ... 
Improving shortest paths in the Delaunay triangulation
Abellanas, Manuel; Claverol Aguas, Mercè; HernándezPeñalver, Gregorio; Hurtado Díaz, Fernando Alfredo; Sacristán Adinolfi, Vera; Saumell Mendiola, Maria; Silveira, Rodrigo Ignacio (2012)
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Open AccessWe study a problem about shortest paths in Delaunay triangulations. Given two nodes s, t in the Delaunay triangulation of a point set P, we look for a new point p that can be added, such that the shortest path from s to ... 
Large bichromatic point sets admit empty monochromatic 4gons
Aichholzer, Oswin; Hackl, Thomas; Huemer, Clemens; Hurtado Díaz, Fernando Alfredo; Vogtenhuber, Birgit (2009)
Conference report
Open AccessWe consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that ...