DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
La geometria computacional, àrea primordial d'actuació del grup, és una disciplina a cavall entre les matemàtiques i la informàtica teòrica. El seu objectiu principal és el disseny i l'anàlisi d'algorismes per a la solució eficient de problemes geomètrics. En conseqüència, una tasca fonamental és la identificació de conceptes, propietats i tècniques que ajudin a la descoberta i implementació d'algorismes eficients. Això comporta l'estudi d'estructures de dades geomètriques, la complexitat d'algorismes, la representació i manipulació de figures i d'objectes, la construcció de llocs geomètrics i, més en general, el desenvolupament de la fonamentació geomètrica. En particular, els problemes estudiats inclouen la cerca i el recompte geomètrics, la convexitat i els processos afins, la proximitat, la intersecció, la triangulació, l'aproximació de formes i la visibilitat. Les àrees principals d'aplicació són la informàtica gràfica, el disseny i la fabricació assistits per ordinador, el reconeixement de formes, la morfologia geomètrica, el disseny VLSI, la visió per computador, els sistemes d'informació geogràfica i la robòtica.
Computational geometry, which is the main area of activity of the group, is a discipline that lies between mathematics and theoretical computer science. The group?s main objective is the design and analysis of algorithms for efficiently solving geometric problems. As a consequence, a fundamental task is to identify concepts, properties and techniques that will help to find and implement efficient geometric algorithms. This involves the study of geometric data structures, algorithm complexity, the representation and manipulation of figures and objects, geometric loci construction and, in general, the development of geometric principles. The problems studied include geometric search and enumeration, convexity and affine processes, proximity, intersection, triangulation, shape approximation and visibility. The main areas of application are computer graphics, computer-aided design and manufacturing, pattern recognition, computational morphology, VLSI design, computer vision, geographical information systems and robotics.
Computational geometry, which is the main area of activity of the group, is a discipline that lies between mathematics and theoretical computer science. The group?s main objective is the design and analysis of algorithms for efficiently solving geometric problems. As a consequence, a fundamental task is to identify concepts, properties and techniques that will help to find and implement efficient geometric algorithms. This involves the study of geometric data structures, algorithm complexity, the representation and manipulation of figures and objects, geometric loci construction and, in general, the development of geometric principles. The problems studied include geometric search and enumeration, convexity and affine processes, proximity, intersection, triangulation, shape approximation and visibility. The main areas of application are computer graphics, computer-aided design and manufacturing, pattern recognition, computational morphology, VLSI design, computer vision, geographical information systems and robotics.
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Articles de revista [85]
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Reports de recerca [14]
Recent Submissions
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Implementing data-dependent triangulations with higher order delaunay triangulations
(Multidisciplinary Digital Publishing Institute (MDPI), 2017-12-01)
Article
Restricted access - publisher's policyThe 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, ... -
Order types of random point sets can be realized with small integer coordinates
(2017)
Conference report
Open AccessLet S := {p1, . . . , pn} be a set of n points chosen independently and uniformly at random from the unit square and let M be a positive integer. For every point pi = (xi , yi) in S, let p 0 i = (bMxic, bMyic). Let S 0 := ... -
Matching points with diametral disks
(2017)
Conference report
Open AccessWe consider matchings between a set R of red points and a set B of blue points with diametral disks. In other words, for each pair of matched points p ¿ R and q ¿ B, we consider the diametral disk defined by p and q. We ... -
The connectivity of the flip graph of Hamiltonian paths of the grid graph
(2017)
Conference report
Open AccessLet Gn,m be the grid graph with n columns and m rows. Let Hn,m be the graph whose vertices are the Hamiltonian paths in Gn,m, where two vertices P1 and P2 are adjacent if we can obtain P2 from P1 by deleting an edge in P1 ... -
Distance 2-domination in prisms of graphs
(2017-01-01)
Article
Open AccessA set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ¿ ( V ( G ) - D ) and D is at most two. Let ¿ 2 ( G ) denote the size of a smallest distance 2 -dominating set of ... -
On Hamiltonian alternating cycles and paths
(2018-03)
Article
Open AccessWe undertake a study on computing Hamiltonian alternating cycles and paths on bicolored point sets. This has been an intensively studied problem, not always with a solution, when the paths and cycles are also required to ... -
Carathodory's theorem in depth
(2017-07-01)
Article
Open AccessLet X be a finite set of points in RdRd . The Tukey depth of a point q with respect to X is the minimum number tX(q)tX(q) of points of X in a halfspace containing q. In this paper we prove a depth version of Carathéodory’s ... -
Characteristic polynomials of production matrices for geometric graphs
(2017-08-01)
Article
Open AccessAn n×n production matrix for a class of geometric graphs has the property that the numbers of these geometric graphs on up to n vertices can be read off from the powers of the matrix. Recently, we obtained such production ... -
Locating domination in bipartite graphs and their complements
(2017-11-03)
Research report
Open AccessA set S of vertices of a graph G is distinguishing if the sets of neighbors in S for every pair of vertices not in S are distinct. A locating-dominating set of G is a dominating distinguishing set. The location-domination ... -
Metric-locating-dominating partitions in graphs
(2017-11-03)
Research report
Open AccessA partition ¿ = { S 1 ,...,S k } of the vertex set of a connected graph G is a metric-locating partition of G if for every pair of vertices u,v belonging to the same part S i , d ( u,S j ) 6 = d ( v,S j ), for some other ... -
Dominating 2- broadcast in graphs: complexity, bounds and extremal graphs
(2017-10-16)
Research report
Open AccessLimited dominating broadcasts were proposed as a variant of dominating broadcasts, where the broadcast function is upper bounded. As a natural extension of domination, we consider dominating 2-broadcasts along with the ... -
Coloración de grafos por vecindades diferentes.
(2017-07-07)
Part of book or chapter of book
Restricted access - publisher's policyEn este trabajo de nimos las coloraciones de un grafo que lo resuelven por vecindad. Notamos NL ( G ) al cardinal m nimo de una de estas coloraciones consideradas del grafo G . Estudiamos propiedades generales de estas ...
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