Clara Grima | Universidad de Sevilla (original) (raw)

Papers by Clara Grima

The problem of computing a representation of the stabbing lines of a set S of segments in the pla... more The problem of computing a representation of the stabbing lines of a set S of segments in the plane was solved by Edelsbrunner et al. We provide efficient algorithms for the following problems: computing the stabbing wedges for S, finding a stabbing wedge for a set of parallel segments with equal length, and computing other stabbers for S such as a double-wedge and a zigzag. The time and space complexities of the algorithms depend on the number of combinatorially different extreme lines, critical lines, and the number of different slopes that appear in S.

Computational Geometry on Surfaces, 2001

Networks, Mar 1, 2007

ABSTRACT The dilation-free graph of a planar point set S is a graph that spans S in such a way th... more ABSTRACT The dilation-free graph of a planar point set S is a graph that spans S in such a way that the distance between two points in the graph is no longer than their planar distance. Metrically speaking, those graphs are equivalent to complete graphs; however they have far fewer edges when considering the Manhattan distance (we give here an upper bound on the number of saved edges). This article provides several theoretical, algorithmic, and complexity features of dilation-free graphs in the l1-metric, giving several construction algorithms and proving some of their properties. Moreover, special attention is paid to the planar case due to its applications in the design of printed circuit boards. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 49(2), 168–174 2007

Computational Geometry on Surfaces, 2001

Actas Del Encuentro De Matematicos Andaluces Vol 2 2001 Isbn 84 472 0290 9 Pags 187 196, 2001

Computational Geometry on Surfaces, 2001

Eprint Arxiv Math 0311228, Nov 13, 2003

We consider whether any two triangulations of a polygon or a point set on a non-planar surface wi... more We consider whether any two triangulations of a polygon or a point set on a non-planar surface with a given metric can be transformed into each other by a sequence of edge flips. The answer is negative in general with some remarkable exceptions, such as polygons on the cylinder, and on the flat torus, and certain configurations of points on the cylinder.

Computational Geometry on Surfaces, 2001

We study the relationship between some alternative definitions of the concept of the width of a c... more We study the relationship between some alternative definitions of the concept of the width of a convex set on the sphere. Those relations allow to characterize whether a convex set on the sphere can pass through a spherical interval by rigid motions. Finally, we give an optimal ...

A well-known measure of the spread of a set is its diameter (ie, the maximum distance between two... more A well-known measure of the spread of a set is its diameter (ie, the maximum distance between two points of the set). Intuitively, a cluster with small diameter has elements that are closely related, while the opposite is true when the diameter is large. This concept has led to ...

Canadian Conference on Computational Geometry, 2000

Discrete Mathematics, 2000

We show that any two outer-triangulations on the same closed surface can be transformed into each... more We show that any two outer-triangulations on the same closed surface can be transformed into each other by a sequence of diagonalips, up to isotopy, if they have a su6ciently large and equal number of vertices. c 2002 Elsevier Science B.V. All rights reserved.

IntroductionSuppose that given a certain set of objects (orobstacles) in the plane, we want to kn... more IntroductionSuppose that given a certain set of objects (orobstacles) in the plane, we want to know, froma given position, which will be the first objectthat we will see if we sweep the plane as a radarstarting from the horizontal line. In [2] we givea partition of the plane (the polar diagram)that records that information when the objectsare points...(x,y)piang (x,y) piFigure

Computational Geometry on Surfaces, 2001

Lecture Notes in Computer Science, 2012

ABSTRACT A graph G is said to be grid locatable if it admits a representation such that vertices ... more ABSTRACT A graph G is said to be grid locatable if it admits a representation such that vertices are mapped to grid points and edges to line segments that avoid grid points but the extremes. Additionally G is said to be properly embeddable in the grid if it is grid locatable and the segments representing edges do not cross each other. We study the area needed to obtain those representations for some graph families.

Lecture Notes in Computer Science, 2008

We study problems that arise in the context of covering certain geometric objects (so-called seed... more We study problems that arise in the context of covering certain geometric objects (so-called seeds, e.g., points or disks) by a set of other geometric objects (a so-called cover, e.g., a set of disks or homothetic triangles). We insist that the interiors of the seeds and the cover elements are pairwise disjoint, but they can touch. We call the contact graph of a cover a cover contact graph (CCG). We are interested in two types of tasks: (a) deciding whether a given seed set has a connected CCG, and (b) deciding whether a given graph has a realization as a CCG on a given seed set. Concerning task (a) we give efficient algorithms for the case that seeds are points and covers are disks or triangles. We show that the problem becomes NP-hard if seeds and covers are disks. Concerning task (b) we show that it is even NP-hard for point seeds and disk covers (given a fixed correspondence between vertices and seeds).

The problem of computing a representation of the stabbing lines of a set S of segments in the pla... more The problem of computing a representation of the stabbing lines of a set S of segments in the plane was solved by Edelsbrunner et al. We provide efficient algorithms for the following problems: computing the stabbing wedges for S, finding a stabbing wedge for a set of parallel segments with equal length, and computing other stabbers for S such as a double-wedge and a zigzag. The time and space complexities of the algorithms depend on the number of combinatorially different extreme lines, critical lines, and the number of different slopes that appear in S.

Computational Geometry on Surfaces, 2001

Networks, Mar 1, 2007

ABSTRACT The dilation-free graph of a planar point set S is a graph that spans S in such a way th... more ABSTRACT The dilation-free graph of a planar point set S is a graph that spans S in such a way that the distance between two points in the graph is no longer than their planar distance. Metrically speaking, those graphs are equivalent to complete graphs; however they have far fewer edges when considering the Manhattan distance (we give here an upper bound on the number of saved edges). This article provides several theoretical, algorithmic, and complexity features of dilation-free graphs in the l1-metric, giving several construction algorithms and proving some of their properties. Moreover, special attention is paid to the planar case due to its applications in the design of printed circuit boards. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 49(2), 168–174 2007

Computational Geometry on Surfaces, 2001

Actas Del Encuentro De Matematicos Andaluces Vol 2 2001 Isbn 84 472 0290 9 Pags 187 196, 2001

Computational Geometry on Surfaces, 2001

Eprint Arxiv Math 0311228, Nov 13, 2003

We consider whether any two triangulations of a polygon or a point set on a non-planar surface wi... more We consider whether any two triangulations of a polygon or a point set on a non-planar surface with a given metric can be transformed into each other by a sequence of edge flips. The answer is negative in general with some remarkable exceptions, such as polygons on the cylinder, and on the flat torus, and certain configurations of points on the cylinder.

Computational Geometry on Surfaces, 2001

We study the relationship between some alternative definitions of the concept of the width of a c... more We study the relationship between some alternative definitions of the concept of the width of a convex set on the sphere. Those relations allow to characterize whether a convex set on the sphere can pass through a spherical interval by rigid motions. Finally, we give an optimal ...

A well-known measure of the spread of a set is its diameter (ie, the maximum distance between two... more A well-known measure of the spread of a set is its diameter (ie, the maximum distance between two points of the set). Intuitively, a cluster with small diameter has elements that are closely related, while the opposite is true when the diameter is large. This concept has led to ...

Canadian Conference on Computational Geometry, 2000

Discrete Mathematics, 2000

We show that any two outer-triangulations on the same closed surface can be transformed into each... more We show that any two outer-triangulations on the same closed surface can be transformed into each other by a sequence of diagonalips, up to isotopy, if they have a su6ciently large and equal number of vertices. c 2002 Elsevier Science B.V. All rights reserved.

IntroductionSuppose that given a certain set of objects (orobstacles) in the plane, we want to kn... more IntroductionSuppose that given a certain set of objects (orobstacles) in the plane, we want to know, froma given position, which will be the first objectthat we will see if we sweep the plane as a radarstarting from the horizontal line. In [2] we givea partition of the plane (the polar diagram)that records that information when the objectsare points...(x,y)piang (x,y) piFigure

Computational Geometry on Surfaces, 2001

Lecture Notes in Computer Science, 2012

ABSTRACT A graph G is said to be grid locatable if it admits a representation such that vertices ... more ABSTRACT A graph G is said to be grid locatable if it admits a representation such that vertices are mapped to grid points and edges to line segments that avoid grid points but the extremes. Additionally G is said to be properly embeddable in the grid if it is grid locatable and the segments representing edges do not cross each other. We study the area needed to obtain those representations for some graph families.

Lecture Notes in Computer Science, 2008

We study problems that arise in the context of covering certain geometric objects (so-called seed... more We study problems that arise in the context of covering certain geometric objects (so-called seeds, e.g., points or disks) by a set of other geometric objects (a so-called cover, e.g., a set of disks or homothetic triangles). We insist that the interiors of the seeds and the cover elements are pairwise disjoint, but they can touch. We call the contact graph of a cover a cover contact graph (CCG). We are interested in two types of tasks: (a) deciding whether a given seed set has a connected CCG, and (b) deciding whether a given graph has a realization as a CCG on a given seed set. Concerning task (a) we give efficient algorithms for the case that seeds are points and covers are disks or triangles. We show that the problem becomes NP-hard if seeds and covers are disks. Concerning task (b) we show that it is even NP-hard for point seeds and disk covers (given a fixed correspondence between vertices and seeds).