10 citations · 18 across the 12 of their papers we have counts for
21 papers
Blocking Delaunay Triangulations from the Exterior
Oswin Aichholzer, Thomas Hackl, Maarten Löffler +4
Given two distinct point sets and in the plane, we say that \emph{blocks} if no two points of are adjacent in any Delaunay triangulation of . Aichholze…
Dynamic Embeddings of Dynamic Single-Source Upward Planar Graphs
Ivor van der Hoog, Irene Parada, Eva Rotenberg
A directed graph is upward planar if it admits a planar embedding such that each edge is -monotone. Unlike planarity testing, upward planarity testing is NP-hard except in r…
Shooting Stars in Simple Drawings of
Oswin Aichholzer, Alfredo García, Irene Parada +2
Simple drawings are drawings of graphs in which two edges have at most one common point (either a common endpoint, or a proper crossing). It has been an open question whether every…
Crossing Numbers of Beyond-Planar Graphs Revisited
Nathan van Beusekom, Irene Parada, Bettina Speckmann
Graph drawing beyond planarity focuses on drawings of high visual quality for non-planar graphs which are characterized by certain forbidden edge configurations. A natural criterio…
Compacting Squares: Input-Sensitive In-Place Reconfiguration of Sliding Squares
Hugo A. Akitaya, Erik D. Demaine, Matias Korman +6
A well-established theoretical model for modular robots in two dimensions are edge-connected configurations of square modules, which can reconfigure through so-called sliding moves…
On Compatible Matchings
Oswin Aichholzer, Alan Arroyo, Zuzana Masárová +5
A matching is compatible to two or more labeled point sets of size with labels if its straight-line drawing on each of these point sets is crossing-free. We stu…
Upward Point Set Embeddings of Paths and Trees
Elena Arseneva, Pilar Cano, Linda Kleist +4
We study upward planar straight-line embeddings (UPSE) of directed trees on given point sets. The given point set has size at least the number of vertices in the tree. For the…
Characterizing Universal Reconfigurability of Modular Pivoting Robots
Hugo A. Akitaya, Erik D. Demaine, Andrei Gonczi +7
We give both efficient algorithms and hardness results for reconfiguring between two connected configurations of modules in the hexagonal grid. The reconfiguration moves that we co…
Crossing-Optimal Extension of Simple Drawings
Robert Ganian, Thekla Hamm, Fabian Klute +2
In extension problems of partial graph drawings one is given an incomplete drawing of an input graph and is asked to complete the drawing while maintaining certain properties.…
Efficient Segment Folding is Hard
Takashi Horiyama, Fabian Klute, Matias Korman +3
We introduce a computational origami problem which we call the segment folding problem: given a set of line-segments in the plane the aim is to make creases along all segments…
Saturated -Plane Drawings with Few Edges
Fabian Klute, Irene Parada
A drawing of a graph is -plane if no edge is crossed more than times. In this paper we study saturated -plane drawings with few edges. This are -plane drawings in whic…
On the Maximum Number of Crossings in Star-Simple Drawings of with No Empty Lens
Stefan Felsner, Michael Hoffmann, Kristin Knorr +1
A star-simple drawing of a graph is a drawing in which adjacent edges do not cross. In contrast, there is no restriction on the number of crossings between two independent edges. W…
New Results in Sona Drawing: Hardness and TSP Separation
Man-Kwun Chiu, Erik D. Demaine, Jenny Diomidova +6
Given a set of point sites, a sona drawing is a single closed curve, disjoint from the sites and intersecting itself only in simple crossings, so that each bounded region of its co…
On the 2-colored crossing number
Oswin Aichholzer, Ruy Fabila-Monroy, Adrian Fuchs +4
Let be a straight-line drawing of a graph. The rectilinear 2-colored crossing number of is the minimum number of crossings between edges of the same color, taken over all p…
Universal Reconfiguration of Facet-Connected Modular Robots by Pivots: The Musketeers
Hugo A. Akitaya, Esther M. Arkin, Mirela Damian +8
We present the first universal reconfiguration algorithm for transforming a modular robot between any two facet-connected square-grid configurations using pivot moves. More precise…
Inserting one edge into a simple drawing is hard
Alan Arroyo, Fabian Klute, Irene Parada +3
A {\em simple drawing} of a graph is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge in the complement o…
Extending Simple Drawings
Alan Arroyo, Martin Derka, Irene Parada
Simple drawings of graphs are those in which each pair of edges share at most one point, either a common endpoint or a proper crossing. In this paper we study the problem of extend…
Graphs with large total angular resolution
Oswin Aichholzer, Matias Korman, Yoshio Okamoto +4
The total angular resolution of a straight-line drawing is the minimum angle between two edges of the drawing. It combines two properties contributing to the readability of a drawi…
Minimal Representations of Order Types by Geometric Graphs
Oswin Aichholzer, Martin Balko, Michael Hoffmann +8
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 ty…
How to Fit a Tree in a Box
Hugo A. Akitaya, Maarten Löffler, Irene Parada
We study compact straight-line embeddings of trees. We show that perfect binary trees can be embedded optimally: a tree with nodes can be drawn on a by grid…
A superlinear lower bound on the number of 5-holes
Oswin Aichholzer, Martin Balko, Thomas Hackl +5
Let be a finite set of points in the plane in general position, that is, no three points of are on a common line. We say that a set of five points from is a -hol…