DSpace Collection:
http://hdl.handle.net/2117/3199
2015-04-26T09:52:48ZColored Ray configurations
http://hdl.handle.net/2117/27279
Title: Colored Ray configurations
Authors: Fabila Monroy, Ruy; Garcia Olaverri, Alfredo Martin; Hurtado, Ferran; Jaume, Rafel; Pérez Lantero, Pablo; Saumell, Maria; Silveira, Rodrigo Ignacio; Tejel Altarriba, Francisco Javier; Urrutia Galicia, Jorge
Abstract: 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 bound on the number of color sequences that can be realized from any xed point set. We also examine se- quences that can be realized regardless of the point set and exhibit negative examples as well. In addition, we provide algorithms to decide whether a sequence is re- alizable from a given point set on a line or in convex position2015-04-13T11:28:47ZA faster algorithm to compute the visibility map of a 1.5D terrain
http://hdl.handle.net/2117/27275
Title: A faster algorithm to compute the visibility map of a 1.5D terrain
Authors: Löffler, Maarten; Saumell, Maria; Silveira, Rodrigo Ignacio
Abstract: Given a 1.5D terrain, i.e., an x -monotone polygonal line in R 2 with n vertices, and 1 m n viewpoints placed on some of the terrain vertices, we study the problem of computing the parts of the terrain that are visible from at least one of the viewpoints. We present an algorithm that runs in O ( n + m log m ) time. This improves over a previous algorithm recently proposed2015-04-13T11:14:57ZRegion-based approximation of probability distributions (for visibility between imprecise points among obstacles)
http://hdl.handle.net/2117/27274
Title: Region-based approximation of probability distributions (for visibility between imprecise points among obstacles)
Authors: Buchin, Kevin; Kostitsyna, Irina; Löffler, Maarten; Silveira, Rodrigo Ignacio
Abstract: Let p and q be two imprecise points, given as prob- ability density functions on R 2 , and let R be a set of n line segments in R 2 . We study the problem of approximating the probability that p and q can see each other; that is, that the segment connecting p and q does not cross any segment of R . To solve this problem, we approximate each density function by a weighted set of polygons; a novel approach to dealing with probability density functions in computational geometry2015-04-13T11:05:24ZOrder types and cross-sections of line arrangements in R^3
http://hdl.handle.net/2117/26484
Title: Order types and cross-sections of line arrangements in R^3
Authors: Aichholzer, Oswin; Fabila-Monroy, Ruy; Hurtado Díaz, Fernando Alfredo; Pérez Lantero, Pablo; Ruiz Vargas, Andrés; Urrutia Galicia, Jorge; Vogtenhuber, Birgit
Abstract: 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 parallel to any line of L, i.e., the proper cross-sections of L.
As a main result we show that the number of different order types that can be obtained as cross-sections of L is O(n9), and that this bound is tight.2015-02-24T12:06:32ZGeometric biplane graphs I: maximal graphs
http://hdl.handle.net/2117/26184
Title: Geometric biplane graphs I: maximal graphs
Authors: Hurtado Díaz, Fernando Alfredo; Garcia Olaverri, Alfredo Martin; Korman Cozzetti, Matias; Matos, Inés P.; Saumell, Maria; Silveira, Rodrigo Ignacio; Tejel Altarriba, Francisco Javier; Tóth, Csaba D.2015-02-02T17:36:02ZGeometric Biplane Graphs II: Graph Augmentation
http://hdl.handle.net/2117/26085
Title: Geometric Biplane Graphs II: Graph Augmentation
Authors: Hurtado Díaz, Fernando Alfredo; Garcia Olaverri, Alfredo Martin; Korman Cozzetti, Matias; Matos, Inés P.; Saumell, Maria; Silveira, Rodrigo Ignacio; Tejel Altarriba, Francisco Javier; Tóth, Csaba D.
Abstract: 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 su ciently large point set admits a 5-connected
biplane graph and that there are arbitrarily large point sets that do not admit any 6-
connected biplane graph. Furthermore, we show that every plane graph (other than a
wheel or a fan) can be augmented into a 4-connected biplane graph. However, there are
arbitrarily large plane graphs that cannot be augmented to a 5-connected biplane graph
by adding pairwise noncrossing edges.2015-01-26T19:01:27ZTerrain visibility with multiple viewpoints
http://hdl.handle.net/2117/25140
Title: Terrain visibility with multiple viewpoints
Authors: Hurtado Díaz, Fernando Alfredo; Löffler, Maarten; Matos, Inés P.; Sacristán Adinolfi, Vera; Saumell, Maria; Silveira, Rodrigo Ignacio; Staals, Frank
Abstract: We study the problem of visibility in polyhedral terrains in the presence of multiple viewpoints. We consider three fundamental visibility structures: the visibility map, the colored visibility map, and the Voronoi visibility map. We study the complexity of each structure for both 1.5D and 2.5D terrains, and provide efficient algorithms to construct them. Our algorithm for the visibility map in 2.5D terrains improves on the only existing algorithm in this setting.2014-12-23T18:23:25ZOn perfect and quasiperfect dominations in graphs
http://hdl.handle.net/2117/24831
Title: On perfect and quasiperfect dominations in graphs
Authors: Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M. Luz2014-11-25T10:36:52ZLD-graphs and global location-domination in bipartite graphs
http://hdl.handle.net/2117/24830
Title: LD-graphs and global location-domination in bipartite graphs
Authors: Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
Abstract: A dominating setS of a graph G is a locating-dominating-set, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locating-dominating sets of minimum cardinality are called LD - codes
and the cardinality of an LD-code is the
location-domination number
,
¿
(
G
).
An LD-set
S
of a graph
G
is
global
if it is an LD-set for both
G
and its complement,
G
. One of the main contributions of this work is the definition of the
LD-graph
,an
edge-labeled graph associated to an LD-set, that will be very helpful to deduce some
properties of location-domination in graphs. Concretely, we use LD-graphs to study
the relation between the location-domination number in a bipartite graph and its
complement2014-11-25T10:34:30ZThe graph distance game and some graph operations
http://hdl.handle.net/2117/24796
Title: The graph distance game and some graph operations
Authors: Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M. Luz
Abstract: In the graph distance game, two players alternate in constructing a max-
imal path. The objective function is the distance between the two endpoints of the
path, which one player tries to maximize and the other tries to minimize. In this paper
we examine the distance game for various graph operations: the join, the corona and
the lexicographic product of graphs. We provide general bounds and exact results for
special graphs2014-11-21T12:24:49ZOn k-enclosing objects in a coloured point set
http://hdl.handle.net/2117/24559
Title: On k-enclosing objects in a coloured point set
Authors: Barba, Luis; Durocher, Stephane; Fraser, Robert; Hurtado Díaz, Fernando Alfredo; Mehrabi, Saeed; Mondal, Debajyoti; Morrison, Jason Morrison; Skala, Matthew; Wahid, Mohammad Abdul
Abstract: We introduce the exact coloured
k
-enclosing object
problem: given a set
P
of
n
points in
R
2
, each of
which has an associated colour in
f
1
;:::;t
g
, and a vec-
tor
c
= (
c
1
;:::;c
t
), where
c
i
2
Z
+
for each 1
i
t
,
nd a region that contains exactly
c
i
points of
P
of
colour
i
for each
i
. We examine the problems of nd-
ing exact coloured
k
-enclosing axis-aligned rectangles,
squares, discs, and two-sided dominating regions in a
t
-coloured point set2014-11-04T19:07:20ZCell-paths in mono- and bichromatic line arrangements in the plane
http://hdl.handle.net/2117/24536
Title: Cell-paths in mono- and bichromatic line arrangements in the plane
Authors: Aichholzer, Oswin; Cardinal, Jean; Hackl, Thomas; Hurtado Díaz, Fernando Alfredo; Korman Cozzetti, Matias; Pilz, Alexander; Silveira, Rodrigo Ignacio; Uehara, Ryuhei; Vogtenhuber, Birgit; Welzl, Emo
Abstract: 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 cell is revisited). When all lines have the same color, and hence the preceding alternating constraint is dropped, we prove that the dual graph of the arrangement always contains a path of length (n2).2014-10-31T18:38:08ZSoftware for discussing parametric polynomial systems : the Gröbner cover
http://hdl.handle.net/2117/24349
Title: Software for discussing parametric polynomial systems : the Gröbner cover
Authors: Montes Lozano, Antonio; Wibmer, Michael
Abstract: We present the canonical Gröbner Cover method for discussing parametric polynomial systems of equations. Its objective is to decompose the parameter space into subsets (segments) for which it exists a generalized reduced Gröbner basis in the whole segment with fixed set of leading power products on it. Wibmer's Theorem guarantees its existence. The Gröbner Cover is designed in a joint paper of the authors, and the Singular grobcov.lib library [15] implementing it, is developed by Montes. The algorithm is canonic and groups the solutions having the same kind of properties into different disjoint segments. Even if the algorithms involved have high complexity, we show how in practice it is effective in many applications of medium difficulty. An interesting application to automatic deduction of geometric theorems is roughly described here, and another one to provide a taxonomy for exact geometrical loci computations, that is experimentally implemented in a web based application using the dynamic geometry software Geogebra, is explained in another session.2014-10-11T15:23:46ZSoftware using the Gröbner cover for geometrical loci computation and classification
http://hdl.handle.net/2117/24171
Title: Software using the Gröbner cover for geometrical loci computation and classification
Authors: Abanades, Miguel A.; Botan, Francisco; Montes Lozano, Antonio; Recio Muñiz, Tomás
Abstract: We describe here a properly recent application of the Gröbner Cover algorithm (GC) providing an algebraic support to Dynamic Geometry computations of geometrical loci. It provides a complete algebraic solution of locus computation as well as a suitable taxonomy allowing to distinguish the nature of the different components. We included a new algorithm Locus into the Singular grobcov.lib library for this purpose. A web prototype has been implemented using it in Geogebra.2014-09-26T08:32:28ZThe degree-diameter problem in maximal bipartite planar graphs
http://hdl.handle.net/2117/24097
Title: The degree-diameter problem in maximal bipartite planar graphs
Authors: Dalfó Simó, Cristina; Huemer, Clemens; Salas, Julian
Abstract: The (A ,D) (degree/diameter) problem consists of finding the largest possible number of vertices n among all the graphs with maximum degree and diameter D. We consider the (A ,D) problem for maximal planar bipartite graphs, that are simple planar graphs in which every face is a quadrangle. We obtain that for the ( , 2) problem, the number of vertices is n = + 2; and for the ( , 3) problem, n = 3 -1 if is odd and n = 3 -2 if is even. Then, we study the general case ( A ,D) and obtain that an upper bound on n is approximately 3(2D+1)( -2)bD/2c,
and another one is C( - 2)bD/2c if D and C is a sufficiently large constant.
Our upper bounds improve for our kind of graphs the one given by Fellows, Hell and Seyffarth for general planar graphs. We also give a lower bound on n for maximal planar bipartite graphs, which is approximately ( - 2)k if D = 2k, and 3( - 3)k if D = 2k + 1, for and D sufficiently large in both cases.2014-09-18T10:55:22Z