Zobrazeno 1 - 10
of 155
pro vyhledávání: '"Pilz, Alexander"'
Autor:
Aichholzer, Oswin, Hackl, Thomas, Löffler, Maarten, Pilz, Alexander, Parada, Irene, Scheucher, Manfred, Vogtenhuber, Birgit
Given two distinct point sets $P$ and $Q$ in the plane, we say that $Q$ \emph{blocks} $P$ if no two points of $P$ are adjacent in any Delaunay triangulation of $P\cup Q$. Aichholzer et al. (2013) showed that any set $P$ of $n$ points in general posit
Externí odkaz:
http://arxiv.org/abs/2210.12015
Topological drawings are representations of graphs in the plane, where vertices are represented by points, and edges by simple curves connecting the points. A drawing is simple if two edges intersect at most in a single point, either at a common endp
Externí odkaz:
http://arxiv.org/abs/2209.03072
Autor:
Aichholzer, Oswin, Arroyo, Alan, Masárová, Zuzana, Parada, Irene, Perz, Daniel, Pilz, Alexander, Tkadlec, Josef, Vogtenhuber, Birgit
Publikováno v:
Journal of Graph Algorithms and Applications, Vol. 26, no. 2, pp. 225-240, 2022
A matching is compatible to two or more labeled point sets of size $n$ with labels $\{1,\dots,n\}$ if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more
Externí odkaz:
http://arxiv.org/abs/2101.03928
We study noncrossing geometric graphs and their disjoint compatible geometric matchings. Given a cycle (a polygon) P we want to draw a set of pairwise disjoint straight-line edges with endpoints on the vertices of P such that these new edges neither
Externí odkaz:
http://arxiv.org/abs/2008.08413
We consider arrangements of $n$ pseudo-lines in the Euclidean plane where each pseudo-line $\ell_i$ is represented by a bi-infinite connected $x$-monotone curve $f_i(x)$, $x \in \mathbb{R}$, s.t.\ for any two pseudo-lines $\ell_i$ and $\ell_j$ with $
Externí odkaz:
http://arxiv.org/abs/2001.08419
Autor:
Pilz, Alexander, Schnider, Patrick
We consider the following problem: Let $\mathcal{L}$ be an arrangement of $n$ lines in $\mathbb{R}^3$ colored red, green, and blue. Does there exist a vertical plane $P$ such that a line on $P$ simultaneously bisects all three classes of points in th
Externí odkaz:
http://arxiv.org/abs/1909.04419
Autor:
Aichholzer, Oswin, Balko, Martin, Hoffmann, Michael, Kynčl, Jan, Mulzer, Wolfgang, Parada, Irene, Pilz, Alexander, Scheucher, Manfred, Valtr, Pavel, Vogtenhuber, Birgit, Welzl, Emo
Publikováno v:
Journal of Graph Algorithms and Applications 24 (2020), no. 4, 551-572
In order to have a compact visualization of the order type of a given point set S, we are interested in geometric graphs on S with few edges that unambiguously display the order type of S. We introduce the concept of exit edges, which prevent the ord
Externí odkaz:
http://arxiv.org/abs/1908.05124
We show that the graph transformation problem of turning a simple graph into an Eulerian one by a minimum number of single edge switches is NP-hard. Further, we show that any simple Eulerian graph can be transformed into any other such graph by a seq
Externí odkaz:
http://arxiv.org/abs/1905.06895
Assume you have a pizza consisting of four ingredients (e.g., bread, tomatoes, cheese and olives) that you want to share with your friend. You want to do this fairly, meaning that you and your friend should get the same amount of each ingredient. How
Externí odkaz:
http://arxiv.org/abs/1904.02502
We use the concept of production matrices to show that there exist sets of $n$ points in the plane that admit $\Omega(42.11^n)$ crossing-free geometric graphs. This improves the previously best known bound of $\Omega(41.18^n)$ by Aichholzer et al. (2
Externí odkaz:
http://arxiv.org/abs/1902.09841