DSpace Collection:
http://hdl.handle.net/2117/3199
Wed, 16 Apr 2014 13:53:25 GMT2014-04-16T13:53:25Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoWitness bar visibility graphs
http://hdl.handle.net/2117/22337
Title: Witness bar visibility graphs
Authors: Cortés, Carmen; Hurtado Díaz, Fernando Alfredo; Márquez, Alberto; Valenzuela, Jesús
Abstract: Bar visibility graphs were introduced in the seventies as a model for some VLSI layout problems.
They have been also studied since then by the graph drawing community, and recently several
generalizations and restricted versions have been proposed.
We introduce a generalization, witness-bar visibility graphs, and we prove that this class encom-
passes all the bar-visibility variations considered so far. In addition, we show that many classes of graphs are contained in this family, including in particular all planar graphs, interval graphs, circular arc graphs and permutation graphsFri, 21 Mar 2014 16:03:37 GMThttp://hdl.handle.net/2117/223372014-03-21T16:03:37ZCortés, Carmen; Hurtado Díaz, Fernando Alfredo; Márquez, Alberto; Valenzuela, JesúsnoBar visibility graphs were introduced in the seventies as a model for some VLSI layout problems.
They have been also studied since then by the graph drawing community, and recently several
generalizations and restricted versions have been proposed.
We introduce a generalization, witness-bar visibility graphs, and we prove that this class encom-
passes all the bar-visibility variations considered so far. In addition, we show that many classes of graphs are contained in this family, including in particular all planar graphs, interval graphs, circular arc graphs and permutation graphsStabbing Segments with Rectilinear Objects
http://hdl.handle.net/2117/21700
Title: Stabbing Segments with Rectilinear Objects
Authors: Claverol Aguas, Mercè; Seara Ojea, Carlos; Garijo, Delia; Korman, M.; Silveira, Rodrigo Ignacio
Abstract: Given a set of n line segments in the plane, we say that a region R of the plane is a stabber if R contains exactly one end point of each segment of the set. In this paper we provide efficient algorithms for determining wheter or not a stabber exists for several shapes of stabbers. Specially, we consider the case in which the stabber can be described as the intersecction of isothetic halfplanes (thus the stabbers are halfplanes, strips, quadrants, 3-sided rectangles, or rectangles). We provided efficient algorithms reporting all combinatorially different stabbers of the shape. The algorithms run in O(n) time (for the halfplane case), O(n logn) time (for strips and quadrants), O(n^2) (for 3-sided rectangles), or O(n^3) time (for rectangles).Fri, 21 Feb 2014 17:24:50 GMThttp://hdl.handle.net/2117/217002014-02-21T17:24:50ZClaverol Aguas, Mercè; Seara Ojea, Carlos; Garijo, Delia; Korman, M.; Silveira, Rodrigo IgnacionoGiven a set of n line segments in the plane, we say that a region R of the plane is a stabber if R contains exactly one end point of each segment of the set. In this paper we provide efficient algorithms for determining wheter or not a stabber exists for several shapes of stabbers. Specially, we consider the case in which the stabber can be described as the intersecction of isothetic halfplanes (thus the stabbers are halfplanes, strips, quadrants, 3-sided rectangles, or rectangles). We provided efficient algorithms reporting all combinatorially different stabbers of the shape. The algorithms run in O(n) time (for the halfplane case), O(n logn) time (for strips and quadrants), O(n^2) (for 3-sided rectangles), or O(n^3) time (for rectangles).The alternating path problem revisited
http://hdl.handle.net/2117/21369
Title: The alternating path problem revisited
Authors: Claverol Aguas, Mercè; Garijo, Delia; Hurtado Díaz, Fernando Alfredo; Lara Cuevas, María Dolores; Seara Ojea, Carlos
Abstract: It is well known that, given "n" red points and "n" blue points on acircle, it is not always possible to find a plane geometric. Hamiltonian alternating path. In this work we prove that if we relax the constraint on the path from being plane to being 1-plane, then the problem always has a solution, and even a Hamiltonian alternating cycle can be obtained on all instances. we also extend this kind of result to other configurations and provide remarks on similar problems.Mon, 27 Jan 2014 11:06:21 GMThttp://hdl.handle.net/2117/213692014-01-27T11:06:21ZClaverol Aguas, Mercè; Garijo, Delia; Hurtado Díaz, Fernando Alfredo; Lara Cuevas, María Dolores; Seara Ojea, CarlosnoIt is well known that, given "n" red points and "n" blue points on acircle, it is not always possible to find a plane geometric. Hamiltonian alternating path. In this work we prove that if we relax the constraint on the path from being plane to being 1-plane, then the problem always has a solution, and even a Hamiltonian alternating cycle can be obtained on all instances. we also extend this kind of result to other configurations and provide remarks on similar problems.New results on stabbing segments with a polygon
http://hdl.handle.net/2117/20930
Title: New results on stabbing segments with a polygon
Authors: Díaz Bañez, José Miguel; Korman Cozzetti, Matías; Pérez Lantero, Pablo; Pilz, Alexander; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio
Abstract: We consider a natural variation of the concept of stabbing a segment by a simple polygon: a segment is stabbed by a simple polygon P if at least one of its two endpoints is contained in P. A segment set S is stabbed by P if every segment of S is stabbed by P. We show that if S is a set of pairwise disjoint segments, the problem of computing the minimum perimeter polygon stabbing S can be solved in polynomial time. We also prove that for general segments the problem is NP-hard. Further, an adaptation of our polynomial-time algorithm solves an open problem posed by Löffler and van Kreveld [Algorithmica 56(2), 236-269 (2010)] about finding a maximum perimeter convex hull for a set of imprecise points modeled as line segments.Thu, 05 Dec 2013 14:38:36 GMThttp://hdl.handle.net/2117/209302013-12-05T14:38:36ZDíaz Bañez, José Miguel; Korman Cozzetti, Matías; Pérez Lantero, Pablo; Pilz, Alexander; Seara Ojea, Carlos; Silveira, Rodrigo IgnacionoConvex hull, Disjoint segments, Line segment, Natural variation, Polynomial-time algorithms, Simple polygonWe consider a natural variation of the concept of stabbing a segment by a simple polygon: a segment is stabbed by a simple polygon P if at least one of its two endpoints is contained in P. A segment set S is stabbed by P if every segment of S is stabbed by P. We show that if S is a set of pairwise disjoint segments, the problem of computing the minimum perimeter polygon stabbing S can be solved in polynomial time. We also prove that for general segments the problem is NP-hard. Further, an adaptation of our polynomial-time algorithm solves an open problem posed by Löffler and van Kreveld [Algorithmica 56(2), 236-269 (2010)] about finding a maximum perimeter convex hull for a set of imprecise points modeled as line segments.Motion planning for 6D manipulation with aerial towed-cable systems
http://hdl.handle.net/2117/20414
Title: Motion planning for 6D manipulation with aerial towed-cable systems
Authors: Manubens Ferriol, Montserrat; Devaurs, Didier; Ros Giralt, Lluís; Cortés, Juan
Abstract: Performing aerial 6-dimensional manipulation using flying robots is a challenging problem, to which only little work has been devoted. This paper proposes a motion planning approach for the reliable 6-dimensional quasi-static manipulation with an aerial towed-cable system. The novelty of this approach lies in the use of a cost-based motion-planning algorithm together
with some results deriving from the static analysis of cable-driven manipulators. Based on the so-called wrench-feasibility
constraints applied to the cable tensions, as well as thrust constraints applied to the flying robots, we formally characterize
the set of feasible configurations of the system. Besides, the expression of these constraints leads to a criterion to evaluate
the quality of a configuration. This allows us to define a cost function over the configuration space, which we exploit to
compute good-quality paths using the T-RRT algorithm. As part of our approach, we also propose an aerial towed-cable system that we name the FlyCrane. It consists of a platform
attached to three flying robots using six fixed-length cables. We validate the proposed approach on two simulated 6-D quasi-static manipulation problems involving such a system, and show the benefit of taking the cost function into account for such motion
planning tasks.Fri, 18 Oct 2013 09:26:46 GMThttp://hdl.handle.net/2117/204142013-10-18T09:26:46ZManubens Ferriol, Montserrat; Devaurs, Didier; Ros Giralt, Lluís; Cortés, Juannoaerospace robotics
planning (artificial intelligence)
robot kinematics
robotsPerforming aerial 6-dimensional manipulation using flying robots is a challenging problem, to which only little work has been devoted. This paper proposes a motion planning approach for the reliable 6-dimensional quasi-static manipulation with an aerial towed-cable system. The novelty of this approach lies in the use of a cost-based motion-planning algorithm together
with some results deriving from the static analysis of cable-driven manipulators. Based on the so-called wrench-feasibility
constraints applied to the cable tensions, as well as thrust constraints applied to the flying robots, we formally characterize
the set of feasible configurations of the system. Besides, the expression of these constraints leads to a criterion to evaluate
the quality of a configuration. This allows us to define a cost function over the configuration space, which we exploit to
compute good-quality paths using the T-RRT algorithm. As part of our approach, we also propose an aerial towed-cable system that we name the FlyCrane. It consists of a platform
attached to three flying robots using six fixed-length cables. We validate the proposed approach on two simulated 6-D quasi-static manipulation problems involving such a system, and show the benefit of taking the cost function into account for such motion
planning tasks.Universal point subsets for planar graphs
http://hdl.handle.net/2117/18077
Title: Universal point subsets for planar graphs
Authors: Angelini, Patrizio; Binucci, Carla; Evans, William; Hurtado Díaz, Fernando Alfredo; Liotta, Giuseppe; Mchedlidze, Tamara; Meijer, Henk; Okamoto, Yoshio
Abstract: A set S of k points in the plane is a universal point subset for a class G of planar graphs if every graph belonging to G admits a planar straight-line drawing such that k of its vertices are represented by the points of S . In this paper we study the following main problem: For a given class of graphs, what is the maximum k such that there exists a universal point subset of size k ? We provide a ⌈ √ n ⌉ lower bound on k for the class of planar graphs with n ver- tices. In addition, we consider the value F ( n; G ) such that every set of F ( n; G ) points in general position is a universal subset for all graphs with n vertices be- longing to the family G , and we establish upper and lower bounds for F ( n; G ) for different families of planar graphs, including 4-connected planar graphs and nested-triangles graphs.Tue, 05 Mar 2013 17:31:44 GMThttp://hdl.handle.net/2117/180772013-03-05T17:31:44ZAngelini, Patrizio; Binucci, Carla; Evans, William; Hurtado Díaz, Fernando Alfredo; Liotta, Giuseppe; Mchedlidze, Tamara; Meijer, Henk; Okamoto, YoshionoA set S of k points in the plane is a universal point subset for a class G of planar graphs if every graph belonging to G admits a planar straight-line drawing such that k of its vertices are represented by the points of S . In this paper we study the following main problem: For a given class of graphs, what is the maximum k such that there exists a universal point subset of size k ? We provide a ⌈ √ n ⌉ lower bound on k for the class of planar graphs with n ver- tices. In addition, we consider the value F ( n; G ) such that every set of F ( n; G ) points in general position is a universal subset for all graphs with n vertices be- longing to the family G , and we establish upper and lower bounds for F ( n; G ) for different families of planar graphs, including 4-connected planar graphs and nested-triangles graphs.Numerical computation of manipulator singularities
http://hdl.handle.net/2117/17988
Title: Numerical computation of manipulator singularities
Authors: Bohigas Nadal, Oriol; Zlatanov, Dimiter; Ros Giralt, Lluís; Manubens Ferriol, Montserrat; Porta Pleite, Josep Maria
Abstract: This paper provides a method to compute all types
of singularities of non-redundant manipulators with non-helical
lower pairs and designated instantaneous input and output
speeds. A system of equations describing each singularity type is
given. Using a numerical method based on linear relaxations,
the configurations in each type are computed independently.
The method is general and complete: it can be applied to
manipulators with arbitrary geometry; and will isolate singu-
larities with the desired accuracy. As an example, the entire
singularity set and its complete classification are computed for
a two-degree-of-freedom mechanism. The complex partition of
the configuration space by various singularities is illustrated by
three-dimensional projections.Tue, 26 Feb 2013 17:48:15 GMThttp://hdl.handle.net/2117/179882013-02-26T17:48:15ZBohigas Nadal, Oriol; Zlatanov, Dimiter; Ros Giralt, Lluís; Manubens Ferriol, Montserrat; Porta Pleite, Josep Marianorobots
PARAULES AUTOR: singularity set computation, non-redundant manipulator, linear relaxation, branch-and-prune methodThis paper provides a method to compute all types
of singularities of non-redundant manipulators with non-helical
lower pairs and designated instantaneous input and output
speeds. A system of equations describing each singularity type is
given. Using a numerical method based on linear relaxations,
the configurations in each type are computed independently.
The method is general and complete: it can be applied to
manipulators with arbitrary geometry; and will isolate singu-
larities with the desired accuracy. As an example, the entire
singularity set and its complete classification are computed for
a two-degree-of-freedom mechanism. The complex partition of
the configuration space by various singularities is illustrated by
three-dimensional projections.A unified method for computing position and orientation workspaces of general Stewart platforms
http://hdl.handle.net/2117/17966
Title: A unified method for computing position and orientation workspaces of general Stewart platforms
Authors: Bohigas Nadal, Oriol; Ros, LLuís; Manubens Ferriol, Montserrat
Abstract: The workspace of a Stewart platform is a complex six-
dimensional volume embedded in the Cartesian space defined b
y
six pose parameters. Because of its large dimension and com-
plex shape, such workspace is difficult to compute and repres
ent,
so that comprehension on its structure is being gained by stu
dy-
ing its three-dimensional slices. While successful method
s have
been given to determine the constant-orientation slice, th
e com-
putation and appropriate visualization of the constant-po
sition
slice (also known as the orientation workspace) has proved t
o
be a challenging task. This paper presents a unified method fo
r
computing both of such slices, and any other ones defined by
fixing three pose parameters, on general Stewart platforms i
n-
volving mechanical limits on the active and passive joints.
Ad-
ditional advantages over previous methods include the abil
ity to
determine all connected components of the workspace, and an
y
motion barriers present in its interior.Mon, 25 Feb 2013 19:09:18 GMThttp://hdl.handle.net/2117/179662013-02-25T19:09:18ZBohigas Nadal, Oriol; Ros, LLuís; Manubens Ferriol, Montserratnomanipulators
multi-robot systems
robot kinematics
PARAULES AUTOR: workspace, Stewart platformThe workspace of a Stewart platform is a complex six-
dimensional volume embedded in the Cartesian space defined b
y
six pose parameters. Because of its large dimension and com-
plex shape, such workspace is difficult to compute and repres
ent,
so that comprehension on its structure is being gained by stu
dy-
ing its three-dimensional slices. While successful method
s have
been given to determine the constant-orientation slice, th
e com-
putation and appropriate visualization of the constant-po
sition
slice (also known as the orientation workspace) has proved t
o
be a challenging task. This paper presents a unified method fo
r
computing both of such slices, and any other ones defined by
fixing three pose parameters, on general Stewart platforms i
n-
volving mechanical limits on the active and passive joints.
Ad-
ditional advantages over previous methods include the abil
ity to
determine all connected components of the workspace, and an
y
motion barriers present in its interior.Navigating the wrench-feasible C-space of cable-driven hexapods
http://hdl.handle.net/2117/17457
Title: Navigating the wrench-feasible C-space of cable-driven hexapods
Authors: Bohigas Nadal, Oriol; Manubens Ferriol, Montserrat; Ros Giralt, Lluís
Abstract: Motion paths of cable-driven hexapods must carefully be planned to ensure that the lengths and tensions of all cables remain within acceptable limits, for a given wrench applied to the platform. The cables cannot go slack –to keep the control of the platform– nor excessively tight –to prevent cable breakage– even in the presence of bounded perturbations of the wrench. This paper proposes a path planning method that accommodates such constraints simultaneously. Given two configurations of the platform, the method attempts to connect them through a path that, at any point, allows the cables to counteract any wrench lying inside a predefined uncertainty region. The resulting C-space is placed in correspondence with a smooth manifold, which allows defining a continuation strategy to search this space systematically from one configuration, until the second configuration is found, or path non-existence is proved by exhaustion of the search. The approach is illustrated on the NIST Robocrane hexapod, but it remains applicable to general cable-driven hexapods, either to navigate their full six-dimensional C-space, or any of its slices.Mon, 21 Jan 2013 18:08:43 GMThttp://hdl.handle.net/2117/174572013-01-21T18:08:43ZBohigas Nadal, Oriol; Manubens Ferriol, Montserrat; Ros Giralt, Lluísnomanipulators
planning (artificial intelligence)
robot kinematics
PARAULES AUTOR: cable-driven hexapod, tendon, wire, higher-dimensional continuation, wrench-feasible C-space, robocraneMotion paths of cable-driven hexapods must carefully be planned to ensure that the lengths and tensions of all cables remain within acceptable limits, for a given wrench applied to the platform. The cables cannot go slack –to keep the control of the platform– nor excessively tight –to prevent cable breakage– even in the presence of bounded perturbations of the wrench. This paper proposes a path planning method that accommodates such constraints simultaneously. Given two configurations of the platform, the method attempts to connect them through a path that, at any point, allows the cables to counteract any wrench lying inside a predefined uncertainty region. The resulting C-space is placed in correspondence with a smooth manifold, which allows defining a continuation strategy to search this space systematically from one configuration, until the second configuration is found, or path non-existence is proved by exhaustion of the search. The approach is illustrated on the NIST Robocrane hexapod, but it remains applicable to general cable-driven hexapods, either to navigate their full six-dimensional C-space, or any of its slices.Planning singularity-free force-feasible paths on the Stewart platform
http://hdl.handle.net/2117/17355
Title: Planning singularity-free force-feasible paths on the Stewart platform
Authors: Bohigas Nadal, Oriol; Manubens Ferriol, Montserrat; Ros Giralt, Lluís
Abstract: This paper provides a method for computing force-feasible paths on the Stewart platform. Given two configurations of the platform, the method attempts to connect them through a path that, at any point, allows the platform to counteract any external wrench lying inside a predefined six-dimensional region. In particular, the Jacobian matrix of the manipulator will be full rank along such path, so that the path will not traverse the forward singularity locus at any point. The path is computed by first characterizing the force-feasible C-space of the manipulator as the solution set of a system of equations, and then using a higher-dimensional continuation technique to explore this set systematically from one configuration, until the second configuration is found. Examples are included that demonstrate the performance of the method on illustrative situations.Mon, 14 Jan 2013 17:43:09 GMThttp://hdl.handle.net/2117/173552013-01-14T17:43:09ZBohigas Nadal, Oriol; Manubens Ferriol, Montserrat; Ros Giralt, Lluísnorobot kinematics
PARAULES AUTOR: singularity-free path planning, higher-dimensional continuation, singularity avoidance, Stewart platformThis paper provides a method for computing force-feasible paths on the Stewart platform. Given two configurations of the platform, the method attempts to connect them through a path that, at any point, allows the platform to counteract any external wrench lying inside a predefined six-dimensional region. In particular, the Jacobian matrix of the manipulator will be full rank along such path, so that the path will not traverse the forward singularity locus at any point. The path is computed by first characterizing the force-feasible C-space of the manipulator as the solution set of a system of equations, and then using a higher-dimensional continuation technique to explore this set systematically from one configuration, until the second configuration is found. Examples are included that demonstrate the performance of the method on illustrative situations.Using Kapur-Sun-Wang algorithm for the Gröbner Cover
http://hdl.handle.net/2117/17089
Title: Using Kapur-Sun-Wang algorithm for the Gröbner Cover
Authors: Montes Lozano, Antonio
Abstract: Kapur-Sun-Wang have recently developed a very efficient algorithm for computing
Comprehensive Gröbner Systems that has moreover the required essential properties
for being used as first step of the Gröbner Cover algorithm. We have implemented and
adapted it inside the Singular grobcov library for computing the Gröbner Cover and there
are evidences that it makes the canonical algorithm much more effective. In this note we
discuss the performance of GC with KSW on a collection of examples.Tue, 11 Dec 2012 07:59:45 GMThttp://hdl.handle.net/2117/170892012-12-11T07:59:45ZMontes Lozano, AntonionoKapur-Sun-Wang have recently developed a very efficient algorithm for computing
Comprehensive Gröbner Systems that has moreover the required essential properties
for being used as first step of the Gröbner Cover algorithm. We have implemented and
adapted it inside the Singular grobcov library for computing the Gröbner Cover and there
are evidences that it makes the canonical algorithm much more effective. In this note we
discuss the performance of GC with KSW on a collection of examples.Parámetros de localización y dominación de un grafo y su complementario
http://hdl.handle.net/2117/16778
Title: Parámetros de localización y dominación de un grafo y su complementario
Authors: Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
Abstract: Dado un grafo G = (V,E), un conjunto S ⊂ V es localiza-dominante si
ϕ ̸= N(u)∩S ̸= N(v)∩S ̸= ϕ para todo u, v ∈ V \S. Notamos λ(G) al cardinal m´ınimo
de estos conjuntos. En este trabajo estudiamos la relaci´on entre λ(G) y λ(G), damos
cotas ajustadas de λ(G)+λ(G) y caracterizamos los grafos que alcanzan dichas cotas.
En particular demostramos que λ(G) y λ(G) a lo sumo difieren en una unidad. En el
caso particular de ser G un ´arbol y G ̸= P2 demostramos que λ(G) ≤ λ(G) ≤ λ(G)+1.Mon, 22 Oct 2012 14:36:01 GMThttp://hdl.handle.net/2117/167782012-10-22T14:36:01ZHernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio ManuelnoDado un grafo G = (V,E), un conjunto S ⊂ V es localiza-dominante si
ϕ ̸= N(u)∩S ̸= N(v)∩S ̸= ϕ para todo u, v ∈ V \S. Notamos λ(G) al cardinal m´ınimo
de estos conjuntos. En este trabajo estudiamos la relaci´on entre λ(G) y λ(G), damos
cotas ajustadas de λ(G)+λ(G) y caracterizamos los grafos que alcanzan dichas cotas.
En particular demostramos que λ(G) y λ(G) a lo sumo difieren en una unidad. En el
caso particular de ser G un ´arbol y G ̸= P2 demostramos que λ(G) ≤ λ(G) ≤ λ(G)+1.Watching systems in complete bipartite graphs
http://hdl.handle.net/2117/16777
Title: Watching systems in complete bipartite graphs
Authors: Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
Abstract: Many problems related to location and domination give raise to different
parameters in graphs. The aim is to determine the location of some facility, object,
item by placing watchers in some vertices of the graph. Watching systems were introduced
by Auger et al. [1] as a generalization of identifying codes, by considering
the possibility of placing one or more watchers in each vertex. In this paper we study
watching systems in complete bipartite graphs.Mon, 22 Oct 2012 14:32:07 GMThttp://hdl.handle.net/2117/167772012-10-22T14:32:07ZHernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio ManuelnoMany problems related to location and domination give raise to different
parameters in graphs. The aim is to determine the location of some facility, object,
item by placing watchers in some vertices of the graph. Watching systems were introduced
by Auger et al. [1] as a generalization of identifying codes, by considering
the possibility of placing one or more watchers in each vertex. In this paper we study
watching systems in complete bipartite graphs.Compatible matchings in geometric graphs
http://hdl.handle.net/2117/15075
Title: Compatible matchings in geometric graphs
Authors: Aichholzer, Oswin; García Olaverri, Alfredo; Hurtado Díaz, Fernando Alfredo; Tejel Altarriba, F. Javier
Abstract: Two non-crossing geometric graphs on the same set of points are compatible if their union
is also non-crossing. In this paper, we prove that every graph G that has an outerplanar embedding
admits a non-crossing perfect matching compatible with G. Moreover, for non-crossing geometric trees
and simple polygons, we study bounds on the minimum number of edges that a compatible non-crossing
perfect matching must share with the tree or the polygon. We also give bounds on the maximal size of
a compatible matching (not necessarily perfect) that is disjoint from the tree or the polygon.Fri, 10 Feb 2012 19:44:15 GMThttp://hdl.handle.net/2117/150752012-02-10T19:44:15ZAichholzer, Oswin; García Olaverri, Alfredo; Hurtado Díaz, Fernando Alfredo; Tejel Altarriba, F. JaviernoTwo non-crossing geometric graphs on the same set of points are compatible if their union
is also non-crossing. In this paper, we prove that every graph G that has an outerplanar embedding
admits a non-crossing perfect matching compatible with G. Moreover, for non-crossing geometric trees
and simple polygons, we study bounds on the minimum number of edges that a compatible non-crossing
perfect matching must share with the tree or the polygon. We also give bounds on the maximal size of
a compatible matching (not necessarily perfect) that is disjoint from the tree or the polygon.Flow computations on imprecise terrains
http://hdl.handle.net/2117/13873
Title: Flow computations on imprecise terrains
Authors: Driemel, Anne; Haverkort, Herman; Löffler, Maarten; Silveira, Rodrigo Ignacio
Abstract: We study water flow computation on imprecise terrains. We
consider two approaches to modeling flow on a terrain: one where water
flows across the surface of a polyhedral terrain in the direction of steepest
descent, and one where water only flows along the edges of a predefined
graph, for example a grid or a triangulation. In both cases each vertex has
an imprecise elevation, given by an interval of possible values, while its
(x, y)-coordinates are fixed. For the first model, we show that the problem
of deciding whether one vertex may be contained in the watershed of
another is NP-hard. In contrast, for the second model we give a simple
O(n log n) time algorithm to compute the minimal and the maximal
watershed of a vertex, where n is the number of edges of the graph.
On a grid model, we can compute the same in O(n) time.Mon, 14 Nov 2011 11:19:51 GMThttp://hdl.handle.net/2117/138732011-11-14T11:19:51ZDriemel, Anne; Haverkort, Herman; Löffler, Maarten; Silveira, Rodrigo IgnacionoWe study water flow computation on imprecise terrains. We
consider two approaches to modeling flow on a terrain: one where water
flows across the surface of a polyhedral terrain in the direction of steepest
descent, and one where water only flows along the edges of a predefined
graph, for example a grid or a triangulation. In both cases each vertex has
an imprecise elevation, given by an interval of possible values, while its
(x, y)-coordinates are fixed. For the first model, we show that the problem
of deciding whether one vertex may be contained in the watershed of
another is NP-hard. In contrast, for the second model we give a simple
O(n log n) time algorithm to compute the minimal and the maximal
watershed of a vertex, where n is the number of edges of the graph.
On a grid model, we can compute the same in O(n) time.