A Software System for Computing Labeled Orthogonal Drawings of Graphs

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Evaluating Animation Parameters for Morphing Edge Drawings

Partial edge drawings (PED) of graphs avoid edge crossings by subdividing each edge into three parts and representing only its stubs, i.e., the parts incident to the end-nodes. The morphing edge drawing model (MED) extends the PED drawing style by animations that smoothly morph each edge between its representation as stubs and the one as a fully drawn segment while avoiding new crossings. Participants of a previous study on MED (Misue and Akasaka, GD19) reported eye straining caused by the animation. We conducted a user study to evaluate how this effect is influenced by varying animation speed and animation dynamic by considering an easing technique that is commonly used in web design. Our results provide indications that the easing technique may help users in executing topology-based tasks accurately. The participants also expressed appreciation for the easing and a preference for a slow animation speed.Comment: Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023

On the Parameterized Complexity of Computing stst-Orientations with Few Transitive Edges

Orienting the edges of an undirected graph such that the resulting digraph satisfies some given constraints is a classical problem in graph theory, with multiple algorithmic applications. In particular, an $st$-orientation orients each edge of the input graph such that the resulting digraph is acyclic, and it contains a single source $s$ and a single sink $t$. Computing an $st$-orientation of a graph can be done efficiently, and it finds notable applications in graph algorithms and in particular in graph drawing. On the other hand, finding an $st$-orientation with at most $k$ transitive edges is more challenging and it was recently proven to be NP-hard already when $k=0$. We strengthen this result by showing that the problem remains NP-hard even for graphs of bounded diameter, and for graphs of bounded vertex degree. These computational lower bounds naturally raise the question about which structural parameters can lead to tractable parameterizations of the problem. Our main result is a fixed-parameter tractable algorithm parameterized by treewidth

On the Parameterized Complexity of Computing st-Orientations with Few Transitive Edges

Orienting the edges of an undirected graph such that the resulting digraph satisfies some given constraints is a classical problem in graph theory, with multiple algorithmic applications. In particular, an st-orientation orients each edge of the input graph such that the resulting digraph is acyclic, and it contains a single source s and a single sink t. Computing an st-orientation of a graph can be done efficiently, and it finds notable applications in graph algorithms and in particular in graph drawing. On the other hand, finding an st-orientation with at most k transitive edges is more challenging and it was recently proven to be NP-hard already when k = 0. We strengthen this result by showing that the problem remains NP-hard even for graphs of bounded diameter, and for graphs of bounded vertex degree. These computational lower bounds naturally raise the question about which structural parameters can lead to tractable parameterizations of the problem. Our main result is a fixed-parameter tractable algorithm parameterized by treewidth

Upward Book Embeddings of st-Graphs

We study k-page upward book embeddings (kUBEs) of st-graphs, that is, book embeddings of single-source single-sink directed acyclic graphs on k pages with the additional requirement that the vertices of the graph appear in a topological ordering along the spine of the book. We show that testing whether a graph admits a kUBE is NP-complete for k >= 3. A hardness result for this problem was previously known only for k = 6 [Heath and Pemmaraju, 1999]. Motivated by this negative result, we focus our attention on k=2. On the algorithmic side, we present polynomial-time algorithms for testing the existence of 2UBEs of planar st-graphs with branchwidth b and of plane st-graphs whose faces have a special structure. These algorithms run in O(f(b)* n+n^3) time and O(n) time, respectively, where f is a singly-exponential function on b. Moreover, on the combinatorial side, we present two notable families of plane st-graphs that always admit an embedding-preserving 2UBE

Colored anchored visibility representations in 2D and 3D space

© 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In a visibility representation of a graph G, the vertices are represented by nonoverlapping geometric objects, while the edges are represented as segments that only intersect the geometric objects associated with their end-vertices. Given a set P of n points, an Anchored Visibility Representation of a graph G with n vertices is a visibility representation such that for each vertex v of G, the geometric object representing v contains a point of P. We prove positive and negative results about the existence of anchored visibility representations under various models, both in 2D and in 3D space. We consider the case when the mapping between the vertices and the points is not given and the case when it is only partially given.Peer ReviewedPostprint (author's final draft

Algorithms and Bounds for Drawing Non-planar Graphs with Crossing-free Subgraphs

We initiate the study of the following problem: Given a non-planar graph G and a planar subgraph S of G, does there exist a straight-line drawing {\Gamma} of G in the plane such that the edges of S are not crossed in {\Gamma} by any edge of G? We give positive and negative results for different kinds of connected spanning subgraphs S of G. Moreover, in order to enlarge the subset of instances that admit a solution, we consider the possibility of bending the edges of G not in S; in this setting we discuss different trade-offs between the number of bends and the required drawing area.Comment: 21 pages, 9 figures, extended version of 'Drawing Non-planar Graphs with Crossing-free Subgraphs' (21st International Symposium on Graph Drawing, 2013