CGA  Computational Geometry and Applications
The research group on Computational Geometry and Applications (CGA) is devoted to carrying out research on computational geometry with a strong emphasis in applications. Computational geometry is an active field in the interface between applied mathematics and computer science that studies algorithmic problems involving discrete geometric objects. The field has applications in robotics, computer graphics, CAD/CAM, integrated circuit design, computer vision, and geographic information science.
The CGA group has the goal of working not only on the design of efficient algorithms, but also on their application to different domains. In particular, we will concentrate on making progress on core geometric problems, and on their applications to two concrete domains: robotics and geographic information science.
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Articles de revista [25]
Recent Submissions

The [Theta]operator and the low hierarchy
(199207)
Research report
Open AccessLong and Sheu in their paper [LS91] introduced a refinement of the low hierarchy based on the [Theta]levels of the polynomial time hierarchy which gives a deeper sight of the internal structure of NP. In this paper we ... 
Matching random colored points with rectangles
(Springer, 2020)
Conference report
Open AccessLet S[0,1]2 be a set of n points, randomly and uniformly selected. Let RB be a random partition, or coloring, of S in which each point of S is included in R uniformly at random with probability 1/2. We study the random ... 
Algorithmic geometry with infinite time computation
(2021)
Conference report
Restricted access  publisher's policy 
On maximumsum matchings of points
(2021)
Conference report
Restricted access  publisher's policyHuemer et al. (Discrete Math., 2019) proved that for any two point sets R and B with R = B, the perfect matching that matches points of R with points of B, and maximizes the total squared Euclidean distance of the ... 
Terrain prickliness: theoretical grounds for high complexity viewsheds
(2021)
Conference report
Open AccessAn important task when working with terrain models is computing viewsheds: the parts of the terrain visible from a given viewpoint. When the terrain is modeled as a polyhedral terrain, the viewshed is composed of the union ... 
Terrain prickliness: theoretical grounds for low complexity viewsheds
(2021)
Conference report
Restricted access  publisher's policy 
Shortest paths in portalgons
(2021)
Conference report
Restricted access  publisher's policy 
Maximum box problem on stochastic points
(Springer Nature, 20211028)
Article
Open AccessGiven a finite set of weighted points in Rd (where there can be negative weights), the maximum box problem asks for an axisaligned rectangle (i.e., box) such that the sum of the weights of the points that it contains is ... 
On (a, k)sets and (a, k)hulls in the plane
(2021)
Conference report
Open AccessThis abstract reports first the study of upper and lower bounds for the maximum number of all the combinatorially different (a, k)sets of an npoint set P in the plane, 0 < a = p and 0 < 2k < n, depending on the ... 
The edge labeling of higher order Voronoi diagrams
(2021)
Conference report
Open AccessWe present an edge labeling of orderk Voronoi diagrams, Vk(S), of point sets S in the plane, and study properties of the regions defined by them. Among them, we show that Vk(S) has a small orientable cycle and path double ... 
A new metamodule design for efficient reconfiguration of modular robots
(Springer Nature, 20210501)
Article
Open AccessWe propose a new metamodule design for two important classes of modular robots. The new metamodule is threedimensional, robust and compact, improving on the previously proposed one. It applies to socalled “edgehinged” ... 
New production matrices for geometric graphs
(Elsevier, 20220115)
Article
Restricted access  publisher's policyWe use production matrices to count several classes of geometric graphs. We present novel production matrices for noncrossing partitions, connected geometric graphs, and kangulations, which provide another, simple and ...