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.

### Recent Submissions

• #### Farthest color Voronoi diagrams: complexity and algorithms ﻿

(Springer, 2021)
Conference report
Restricted access - publisher's policy
The farthest-color Voronoi diagram (FCVD) is a farthestsite Voronoi structure defined on a family P of m point-clusters in the plane, where the total number of points is n. The FCVD finds applications in problems related ...
• #### Efficient computation of minimum-area rectilinear convex hull under rotation and generalizations ﻿

(Springer Nature, 2021-03)
Article
Restricted access - publisher's policy
Let P be a set of n points in the plane. We compute the value of ¿¿[0,2p) for which the rectilinear convex hull of P, denoted by RHP(¿), has minimum (or maximum) area in optimal O(nlogn) time and O(n) space, improving the ...
• #### Caterpillars are antimagic ﻿

(2021-01-21)
Article
Restricted access - publisher's policy
An antimagic labeling of a graph G is a bijection from the set of edges E(G) to {1,2,…,|E(G)|}, such that all vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of the labels assigned to the ...
• #### Flips in higher order Delaunay triangulations ﻿

(2021)
Conference report
Restricted access - publisher's policy
We study the flip graph of higher order Delaunay triangulations. A triangulation of a set S of n points in the plane is order-k Delaunay if for every triangle its circumcircle encloses at most k points of S. The flip graph ...
• #### Affine invariant triangulations ﻿

(2019)
Conference report
Restricted access - publisher's policy
We study affine invariant 2D triangulation methods. That is, methods that produce the same triangulation for a point set S for any (unknown) affine transformation of S. Our work is based on a method by Nielson [A ...
• #### Hamiltonicity for convex shape Delaunay and Gabriel Graphs ﻿

(Springer, 2019)
Conference report
Restricted access - publisher's policy
We study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Instead of defining these proximity graphs using circles, we use an arbitrary convex shape C. Let S be a point set in the plane. ...
• #### Hamiltonicity for convex shape Delaunay and Gabriel graphs ﻿

(2019)
Conference report
Restricted access - publisher's policy
We study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Let S be a point set in the plane. The k-order Delaunay graph of S, denoted k-DGC(S), has vertex set S and edge pq provided ...
• #### Map construction algorithms: a local evaluation through hiking data ﻿

(2020-02-26)
Article
Open Access
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 ...
• #### Hamiltonicity for convex shape Delaunay and Gabriel graphs ﻿

(2020-08)
Article
Restricted access - publisher's policy
We study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Instead of defining these proximity graphs using circles, we use an arbitrary convex shape $$\mathcal {C}$$ . Let S be a point ...
• #### Convex quadrangulations of bichromatic point sets ﻿

(2020-06-05)
Article
Restricted access - publisher's policy
We consider quadrangulations of red and blue points in the plane where each face is convex and no edge connects two points of the same color. In particular, we show that the following problem is NP-hard: Given a finite set ...
• #### Total domination in plane triangulations ﻿

(2020-11-09)
External research report
Open Access
• #### Characterizations of some complexity classes between [theta sub 2 super p] and [delta sub 2 super p] ﻿

(1990)
External research report
Open Access
We give some characterizations of the classes P super NP [0(log super k n)]. First, we show that these classes are equal to classes AC super k-1 (N P). Second, we prove that they are also equivalent to some classes defined ...