1. Conjunts numèrics

2022/202

Fonaments matemàtics : àlgebra i Càlcul

2013/201

Estadística : problemes resolts

Contingut:1 Probabilitat 2 Combinatòria 3 Models de probabilitat discrets 4 Models de probabilitat continus 5 Mostreig 6 Estimadors 7 Intervals de confiança 8 Contrast d'Hipòtesi 9 Exàmens 10 Bibliografia2016/201

GD Geometria per al disseny. Pràctiques

2022/202

Introducció a la lògica

2013/201

Point set stratification and minimum weight structures

Three different concepts of depth in a point set are considered and compared: Convex depth, location depth and Delaunay depth. As a notion of weight is naturally associated to each depth definition, we also present results on minimum weight structures (like spanning trees, poligonizations and triangulations) with respect to the three variations.DURSYMinisterio de Ciencia y Tecnologí

Properties for Voronoi diagrams of arbitrary order on the sphere

For a given set of points U on a sphere S, the order k spherical Voronoi diagram SV_k(U) decomposes the surface of S into regions whose points have the same k nearest points of U. We study properties for SV_k(U), using different tools: the geometry of the sphere, a labeling for the edges of SV_k(U), and the inversion transformation. Hyeon-Suk Na, Chung-Nim Lee, and Otfried Cheong (Comput. Geom., 2002) applied inversions to construct SV_1(U). We generalize their construction for spherical Voronoi diagrams from order 1 to any order k. We use that construction to prove formulas for the numbers of vertices, edges, and faces in SV_k(U). Among the properties of SV_k(U), we also show that SV_k(U) has a small orientable cycle double cover.Postprint (published version

Metric dimension of maximal outerplanar graphs

In this paper, we study the metric dimension problem in maximal outerplanar graphs. Concretely, if ß(G) denotes the metric dimension of a maximal outerplanar graph G of order n, we prove that 2=ß(G)=¿2n5¿ and that the bounds are tight. We also provide linear algorithms to decide whether the metric dimension of G is 2 and to build a resolving set S of size ¿2n5¿ for G. Moreover, we characterize all maximal outerplanar graphs with metric dimension 2.Peer ReviewedPostprint (author's final draft

Stabbers of line segments in the plane

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.Preprin

On Hamiltonian alternating cycles and paths

We 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 be plane. In this paper, we relax the constraint on the cycles and paths from being plane to being 1-plane, and deal with the same type of questions as those for the plane case, obtaining a remarkable variety of results. For point sets in general position, our main result is that it is always possible to obtain a 1-plane Hamiltonian alternating cycle. When the point set is in convex position, we prove that every Hamiltonian alternating cycle with minimum number of crossings is 1-plane, and provide O(n) and O(n2) time algorithms for computing, respectively, Hamiltonian alternating cycles and paths with minimum number of crossings.Peer ReviewedPostprint (author's final draft