Cologne Excellence Cluster on Cellular Stress Responses in Aging Associated Diseases
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On the Density of Maximal 1-Planar Graphs
No full textA graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. It is maximal 1-planar if the addition of any edge violates 1-planarity.
Maximal 1-planar graphs have at most 4n−8 edges. We show that there are sparse maximal 1-planar graphs with only edges. With a fixed rotation system there are maximal 1-planar graphs with only edges. This is sparser than maximal planar graphs. There cannot be maximal 1-planar graphs with less than edges and less than edges with a fixed rotation system. Furthermore, we prove that a maximal 1-planar rotation system of a graph uniquely determines its 1-planar embedding
Mental Map Preservation Helps User Orientation in Dynamic Graphs
No full textWe present the results of a formal experiment that tests the ability of a participant to orient themselves in a dynamically evolving graph. Examples of these tasks include finding a specific location or route between two locations. We find that preserving the mental map for the tasks tested is significantly faster and produces fewer errors. As the number of targets increase, this result holds
Time-Space Maps from Triangulations
No full textTime-space maps show travel time as distances on a map. We discuss the case of time-space maps with a single center; here the travel times from a single source location to a number of destinations are shown by their distances. To accomplish this while maintaining recognizability, the input map must be deformed in a suitable manner. We present three different methods and analyze them experimentally
Graph Drawing through the Lens of a Framework for Analyzing Visualization Methods (Invited Talk, Extended Abstract)
No full textThe visualization community has drawn heavily on the algorithmic and systems-building work that has appeared with the graph drawing literature, and in turn has been a fertile source of applications. In the spirit of further promoting the effective transfer of ideas between our two communities, I will discuss a framework for analyzing the design of visualization systems. I will then analyze a range of graph drawing techniques through this lens. In the early stages of a project, this sort of analysis may benefit algorithm developers who seek to identify open problems to attack. In later project stages, it could guide algorithm developers in characterizing how newly developed layout methods connect with the tasks and goals of target users in different application domains
Plane Cubic Graphs and the Air-Pressure Method
No full textThomassen[1] proved that plane cubic graphs are area-universal, i.e., for a plane cubic graph G with prescribed face areas there exists a stright-line (re-)drawing G’ that realizes these areas. Thomassen uses induction and proves the existence of a degenerate drawing where distinct vertices may be placed at the same position. We show that the plane cubic graphs are area-universal using the air-pressure method. In [2,3], a similar method has been applied in the context of area-universality of rectangular layouts. With the poster, we give the idea of how the method can be adapted for other classes of plane graphs, in particular for plane cubic graphs
The First Simple Symmetric 11-Venn Diagram
No full textAn n-Venn diagram is a collection of n simple closed curves in the plane with the following properties: (a) Each of the different intersections of the open interiors or exteriors of the curves is a non-empty connected region; (b) there are only finitely many points where the curves intersect. If each of the intersections is of only two curves, then the diagram is said to be simple. The purpose of this poster is to highlight how we discovered the first simple symmetric 11-Venn diagram
Planar and Plane Slope Number of Partial 2-Trees
No full textWe prove tight bounds (up to a small multiplicative or additive constant) for the plane and the planar slope numbers of partial 2-trees of bounded degree. As a byproduct of our techniques, we answer a long standing question by Garg and Tamassia about the angular resolution of the planar straight-line drawings of series-parallel graphs of bounded degree
Incremental Grid-Like Layout Using Soft and Hard Constraints
No full textWe explore various techniques to incorporate grid-like layout conventions into a force-directed, constraint-based graph layout framework. In doing so we are able to provide high-quality layout—with predominantly axis-aligned edges—that is more flexible than previous grid-like layout methods and which can capture layout conventions in notations such as SBGN (Systems Biology Graphical Notation). Furthermore, the layout is easily able to respect user-defined constraints and adapt to interaction in online systems and diagram editors such as Dunnart
3D Graph Printing in GLuskap
No full textThe GLuskap software package for creating and editing graphs in 3D has been extended to include 3D printing of graphs by exporting the graph to a common file format capable of being printed on most commercially available 3D printers