Ponències/Comunicacions de congressos
http://hdl.handle.net/2117/3199
2017-12-16T05:33:59ZLocation in maximal outerplanar graphs
http://hdl.handle.net/2117/107909
Location in maximal outerplanar graphs
Claverol Aguas, Mercè; García, Alfredo; Hernández, Gregorio; Hernando Martín, María del Carmen; Maureso Sánchez, Montserrat; Mora Giné, Mercè; Tejel, Javier
In this work we study the metric dimension and the
location-domination number of maximal outerplanar
graphs. Concretely, we determine tight upper and
lower bounds on the metric dimension and characterize
those maximal outerplanar graphs attaining the
lower bound. We also give a lower bound on the
location-domination number of maximal outerplanar
graphs.
2017-09-22T11:18:42ZClaverol Aguas, MercèGarcía, AlfredoHernández, GregorioHernando Martín, María del CarmenMaureso Sánchez, MontserratMora Giné, MercèTejel, JavierIn this work we study the metric dimension and the
location-domination number of maximal outerplanar
graphs. Concretely, we determine tight upper and
lower bounds on the metric dimension and characterize
those maximal outerplanar graphs attaining the
lower bound. We also give a lower bound on the
location-domination number of maximal outerplanar
graphs.Locating-dominating partitions in graphs
http://hdl.handle.net/2117/104422
Locating-dominating partitions in graphs
Pelayo Melero, Ignacio Manuel; Hernando Martín, María del Carmen; Mora Giné, Mercè
Let G = (V, E) be a connected graph of order n. Let ¿ = {S1, . . . , Sk} be
a partition of V . Let r(u|¿) denote the vector of distances between a vertex
v ¿ V and the elements of ¿, that is, r(v, ¿) = (d(v, S1), . . . , d(v, Sk)). The
partition ¿ is called a locating partition of G if, for every pair of distinct
vertices u, v ¿ V , r(u, ¿) 6= r(v, ¿). A locating partition ¿ is called metriclocating-dominating partition (an MLD-partition for short) of G if it is also dominating,
2017-05-15T12:02:03ZPelayo Melero, Ignacio ManuelHernando Martín, María del CarmenMora Giné, MercèLet G = (V, E) be a connected graph of order n. Let ¿ = {S1, . . . , Sk} be
a partition of V . Let r(u|¿) denote the vector of distances between a vertex
v ¿ V and the elements of ¿, that is, r(v, ¿) = (d(v, S1), . . . , d(v, Sk)). The
partition ¿ is called a locating partition of G if, for every pair of distinct
vertices u, v ¿ V , r(u, ¿) 6= r(v, ¿). A locating partition ¿ is called metriclocating-dominating partition (an MLD-partition for short) of G if it is also dominating,Map construction algorithms: an evaluation through hiking data
http://hdl.handle.net/2117/103775
Map construction algorithms: an evaluation through hiking data
Duran, David; Sacristán Adinolfi, Vera; Silveira, Rodrigo Ignacio
We study five existing map construction algorithms, designed and tested with urban vehicle data in mind, and apply them to hiking trajectories with different terrain characteristics. Our main goal is to better understand the existing algorithms and to what extent they apply in a wider context. Indeed, our data differs from the one previously used to evaluate map construction algorithm in several aspects: higher GPS error, narrow and winding paths, and trajectories with its own characteristics in terms of speed or direction. We have chosen four different areas of varied geographic features. For each of them we have considered a set of hiking GPS trajectories, each with a total number of nodes between 38,000 and 288,000. For each algorithm we have analyzed the parameters it uses, and adjusted them to each data set. We present an analysis of the generated maps produced by each algorithm on each data set, and a discussion of the most important artifacts detected. We consider that this analysis sheds new light into the current challenges for map construction algorithms, and will be of help for designing new and better methods.
2017-04-27T10:27:51ZDuran, DavidSacristán Adinolfi, VeraSilveira, Rodrigo IgnacioWe study five existing map construction algorithms, designed and tested with urban vehicle data in mind, and apply them to hiking trajectories with different terrain characteristics. Our main goal is to better understand the existing algorithms and to what extent they apply in a wider context. Indeed, our data differs from the one previously used to evaluate map construction algorithm in several aspects: higher GPS error, narrow and winding paths, and trajectories with its own characteristics in terms of speed or direction. We have chosen four different areas of varied geographic features. For each of them we have considered a set of hiking GPS trajectories, each with a total number of nodes between 38,000 and 288,000. For each algorithm we have analyzed the parameters it uses, and adjusted them to each data set. We present an analysis of the generated maps produced by each algorithm on each data set, and a discussion of the most important artifacts detected. We consider that this analysis sheds new light into the current challenges for map construction algorithms, and will be of help for designing new and better methods.Implementing data-dependent triangulations with higher order Delaunay triangulations
http://hdl.handle.net/2117/103687
Implementing data-dependent triangulations with higher order Delaunay triangulations
Rodríguez, Natalia; Silveira, Rodrigo Ignacio
The Delaunay triangulation is the standard choice for building triangulated irregular networks (TINs) to represent terrain surfaces. However, the Delaunay triangulation is based only on the 2D coordinates of the data points, ignoring their elevation. It has long been recognized that sometimes it may be beneficial to use other, non-Delaunay, criteria to build TINs. Data-dependent triangulations were introduced decades ago to address this. However, they are rarely used in practice, mostly because the optimization of data- dependent criteria often results in triangulations with many thin and elongated triangles. Recently, in the field of computational geometry, higher order Delaunay triangulations (HODTs) were introduced, trying to tackle both issues at the same time-data-dependent criteria and good triangle shape. Nevertheless, most previous studies about them have been limited to theoretical aspects. In this work we present the first extensive experimental study on the practical use of HODTs, as a tool to build data-dependent TINs. We present experiments with two USGS terrains that show that HODTs can give significant improvements over the Delaunay triangulation for the criteria identified as most important for data-dependent triangulations. The resulting triangulations have data-dependent values comparable to those obtained with pure data-dependent approaches, without compromising the shape of the triangles, and are faster to compute.
2017-04-25T08:25:55ZRodríguez, NataliaSilveira, Rodrigo IgnacioThe Delaunay triangulation is the standard choice for building triangulated irregular networks (TINs) to represent terrain surfaces. However, the Delaunay triangulation is based only on the 2D coordinates of the data points, ignoring their elevation. It has long been recognized that sometimes it may be beneficial to use other, non-Delaunay, criteria to build TINs. Data-dependent triangulations were introduced decades ago to address this. However, they are rarely used in practice, mostly because the optimization of data- dependent criteria often results in triangulations with many thin and elongated triangles. Recently, in the field of computational geometry, higher order Delaunay triangulations (HODTs) were introduced, trying to tackle both issues at the same time-data-dependent criteria and good triangle shape. Nevertheless, most previous studies about them have been limited to theoretical aspects. In this work we present the first extensive experimental study on the practical use of HODTs, as a tool to build data-dependent TINs. We present experiments with two USGS terrains that show that HODTs can give significant improvements over the Delaunay triangulation for the criteria identified as most important for data-dependent triangulations. The resulting triangulations have data-dependent values comparable to those obtained with pure data-dependent approaches, without compromising the shape of the triangles, and are faster to compute.Stabbing circles for some sets of Delaunay segments
http://hdl.handle.net/2117/102530
Stabbing circles for some sets of Delaunay segments
Claverol Aguas, Mercè; Khramtcova, Elena; Papadopoulou, Evanthia; Saumell, Maria; Seara Ojea, Carlos
Let S be a set of n segments in the plane such that, for
every segment, its two endpoints are adjacent in the Delaunay triangulation of the set of endpoints of all segments in S. Our goal is to compute all the combinatorially different stabbing circles for S, and the ones with maximum and minimum radius. We exploit a recent result to solve this problem in O(n log n) in two particular cases: (i) all segments in S are parallel; (ii) all segments in S have the same length. We also show that the problem of computing the stabbing circle of minimum radius of a set of n parallel segments of equal length (not necessarily satisfying the Delaunay condition) has an Omega(n log n) lower bound.
2017-03-15T15:55:08ZClaverol Aguas, MercèKhramtcova, ElenaPapadopoulou, EvanthiaSaumell, MariaSeara Ojea, CarlosLet S be a set of n segments in the plane such that, for
every segment, its two endpoints are adjacent in the Delaunay triangulation of the set of endpoints of all segments in S. Our goal is to compute all the combinatorially different stabbing circles for S, and the ones with maximum and minimum radius. We exploit a recent result to solve this problem in O(n log n) in two particular cases: (i) all segments in S are parallel; (ii) all segments in S have the same length. We also show that the problem of computing the stabbing circle of minimum radius of a set of n parallel segments of equal length (not necessarily satisfying the Delaunay condition) has an Omega(n log n) lower bound.Stabbing circles for sets of segments in the plane
http://hdl.handle.net/2117/102514
Stabbing circles for sets of segments in the plane
Claverol Aguas, Mercè; Khramtcova, Elena; Papadopoulou, Evanthia; Saumell, Maria; Seara Ojea, Carlos
Stabbing a set S of n segments in the plane by a line is a well-known problem. In this paper we consider the
variation where the stabbing object is a circle instead of a line. We show that the problem is tightly connected to cluster Voronoi diagrams, in particular, the Hausdorff and the farthest-color Voronoi diagram. Based on these diagrams, we provide a method to compute all the combinatorially different stabbing circles for S, and the stabbing circles with maximum and minimum radius. We give conditions under which our method is fast. These conditions are satisfied if the segments in S are parallel, resulting in a Onlog2n) time algorithm. We also observe that the stabbing circle problem for S can be solved in optimal O(n2) time and space by reducing the problem to computing the stabbing planes for a set of segments in 3D.
2017-03-15T13:04:35ZClaverol Aguas, MercèKhramtcova, ElenaPapadopoulou, EvanthiaSaumell, MariaSeara Ojea, CarlosStabbing a set S of n segments in the plane by a line is a well-known problem. In this paper we consider the
variation where the stabbing object is a circle instead of a line. We show that the problem is tightly connected to cluster Voronoi diagrams, in particular, the Hausdorff and the farthest-color Voronoi diagram. Based on these diagrams, we provide a method to compute all the combinatorially different stabbing circles for S, and the stabbing circles with maximum and minimum radius. We give conditions under which our method is fast. These conditions are satisfied if the segments in S are parallel, resulting in a Onlog2n) time algorithm. We also observe that the stabbing circle problem for S can be solved in optimal O(n2) time and space by reducing the problem to computing the stabbing planes for a set of segments in 3D.A new meta-module for efficient reconfiguration of hinged-units modular robots
http://hdl.handle.net/2117/100623
A new meta-module for efficient reconfiguration of hinged-units modular robots
Parada, Irene; Sacristán Adinolfi, Vera; Silveira, Rodrigo Ignacio
We present a robust and compact meta-module for edge-hinged modular robot units such as M-TRAN,
SuperBot, SMORES, UBot, PolyBot and CKBot, as well as for central-point-hinged ones such as Molecubes and
Roombots. Thanks to the rotational degrees of freedom of these units, the novel meta-module is able to expand
and contract, as to double/halve its length in each dimension. Moreover, for a large class of edge-hinged robots the
proposed meta-module also performs the scrunch/relax and transfer operations required by any tunneling-based
reconfiguration strategy, such as those designed for Crystalline and Telecube robots. These results make it possible to
apply efficient geometric reconfiguration algorithms to this type of robots. We prove the size of this new meta-module to
be optimal. Its robustness and performance substantially improve over previous results.
2017-02-07T12:20:38ZParada, IreneSacristán Adinolfi, VeraSilveira, Rodrigo IgnacioWe present a robust and compact meta-module for edge-hinged modular robot units such as M-TRAN,
SuperBot, SMORES, UBot, PolyBot and CKBot, as well as for central-point-hinged ones such as Molecubes and
Roombots. Thanks to the rotational degrees of freedom of these units, the novel meta-module is able to expand
and contract, as to double/halve its length in each dimension. Moreover, for a large class of edge-hinged robots the
proposed meta-module also performs the scrunch/relax and transfer operations required by any tunneling-based
reconfiguration strategy, such as those designed for Crystalline and Telecube robots. These results make it possible to
apply efficient geometric reconfiguration algorithms to this type of robots. We prove the size of this new meta-module to
be optimal. Its robustness and performance substantially improve over previous results.Ramsey numbers for empty convex polygons
http://hdl.handle.net/2117/85553
Ramsey numbers for empty convex polygons
Bautista-Santiago, Crevel; Cano, Javier; Fabila-Monroy, Ruy; Hidalgo-Toscano, Carlos; Huemer, Clemens; Leaños, Jesús; Sakai, Toshinori; Urrutia, Jorge
We study a geometric Ramsey type problem where the vertices of the complete graph Kn are placed on a set S of n points in general position in the plane, and edges are drawn as straight-line segments. We define the empty convex polygon Ramsey number REC (k, k) as the smallest number n such that for every set S of n points and for every two-coloring of the edges of Kn drawn on S, at least one color class contains an empty convex k-gon. A polygon is empty if it contains no points from S in its interior. We prove 17 ≤ REC (3, 3) ≤ 463 and 57 ≤ REC (4, 4). Further, there are three-colorings of the edges of Kn (drawn on a set S) without empty monochromatic triangles. A related Ramsey number for islands in point sets is also studied.
2016-04-12T11:19:04ZBautista-Santiago, CrevelCano, JavierFabila-Monroy, RuyHidalgo-Toscano, CarlosHuemer, ClemensLeaños, JesúsSakai, ToshinoriUrrutia, JorgeWe study a geometric Ramsey type problem where the vertices of the complete graph Kn are placed on a set S of n points in general position in the plane, and edges are drawn as straight-line segments. We define the empty convex polygon Ramsey number REC (k, k) as the smallest number n such that for every set S of n points and for every two-coloring of the edges of Kn drawn on S, at least one color class contains an empty convex k-gon. A polygon is empty if it contains no points from S in its interior. We prove 17 ≤ REC (3, 3) ≤ 463 and 57 ≤ REC (4, 4). Further, there are three-colorings of the edges of Kn (drawn on a set S) without empty monochromatic triangles. A related Ramsey number for islands in point sets is also studied.On the disks with diameters the sides of a convex 5-gon
http://hdl.handle.net/2117/85548
On the disks with diameters the sides of a convex 5-gon
Huemer, Clemens; Pérez-Lantero, Pablo
We prove that for any convex pentagon there are two disks, among the five disks having a side of the pentagon as diameter and the midpoint of the side as its center, that do not intersect. This shows that K5 is never the intersection graph of such five disks.
2016-04-12T10:55:15ZHuemer, ClemensPérez-Lantero, PabloWe prove that for any convex pentagon there are two disks, among the five disks having a side of the pentagon as diameter and the midpoint of the side as its center, that do not intersect. This shows that K5 is never the intersection graph of such five disks.Region-based approximation algorithms for visibility between imprecise locations
http://hdl.handle.net/2117/82487
Region-based approximation algorithms for visibility between imprecise locations
Buchin, Kevin; Kostitsyna, Irina; Löffler, Maarten; Silveira, Rodrigo Ignacio
In this paper we present new geometric algorithms for approximating the visibility between two imprecise locations amidst a set of obstacles, where the imprecise locations are modeled by continuous probability distributions. Our techniques are based on approximating distributions by a set of regions rather than on approximating by a discrete point sample. In this way we obtain guaranteed error bounds, and the results are more robust than similar results based on discrete point sets. We implemented our techniques and present an experimental evaluation. The experiments show that the actual error of our region-based approximation scheme converges quickly when increasing the complexity of the regions.
2016-02-03T11:58:09ZBuchin, KevinKostitsyna, IrinaLöffler, MaartenSilveira, Rodrigo IgnacioIn this paper we present new geometric algorithms for approximating the visibility between two imprecise locations amidst a set of obstacles, where the imprecise locations are modeled by continuous probability distributions. Our techniques are based on approximating distributions by a set of regions rather than on approximating by a discrete point sample. In this way we obtain guaranteed error bounds, and the results are more robust than similar results based on discrete point sets. We implemented our techniques and present an experimental evaluation. The experiments show that the actual error of our region-based approximation scheme converges quickly when increasing the complexity of the regions.