356 research outputs found
Mixed Linear Layouts of Planar Graphs
A -stack (respectively, -queue) layout of a graph consists of a total
order of the vertices, and a partition of the edges into sets of
non-crossing (non-nested) edges with respect to the vertex ordering. In 1992,
Heath and Rosenberg conjectured that every planar graph admits a mixed
-stack -queue layout in which every edge is assigned to a stack or to a
queue that use a common vertex ordering.
We disprove this conjecture by providing a planar graph that does not have
such a mixed layout. In addition, we study mixed layouts of graph subdivisions,
and show that every planar graph has a mixed subdivision with one division
vertex per edge.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
On Minimizing Crossings in Storyline Visualizations
In a storyline visualization, we visualize a collection of interacting
characters (e.g., in a movie, play, etc.) by -monotone curves that converge
for each interaction, and diverge otherwise. Given a storyline with
characters, we show tight lower and upper bounds on the number of crossings
required in any storyline visualization for a restricted case. In particular,
we show that if (1) each meeting consists of exactly two characters and (2) the
meetings can be modeled as a tree, then we can always find a storyline
visualization with crossings. Furthermore, we show that there
exist storylines in this restricted case that require
crossings. Lastly, we show that, in the general case, minimizing the number of
crossings in a storyline visualization is fixed-parameter tractable, when
parameterized on the number of characters . Our algorithm runs in time
, where is the number of meetings.Comment: 6 pages, 4 figures. To appear at the 23rd International Symposium on
Graph Drawing and Network Visualization (GD 2015
Drawing Layered Hypergraphs
Orthogonally drawn hypergraphs have important applications, e.g. in actor-oriented data flow diagrams for modeling complex software systems. Graph drawing algorithms based on the approach by Sugiyama et al. place nodes into consecutive layers and try to minimize the number of edge crossings by finding suitable orderings of the nodes in each layer. With orthogonal hyperedges, however, the exact number of crossings is not determined until the edges are actually routed in a later phase of the algorithm, which makes it hard to evaluate the quality of a given node ordering beforehand. In this report, we present and evaluate two crossing counting algorithms that predict the number of crossings between orthogonally routed hyperedges much more accurately than previous methods. We also describe methods for routing hyperedges that span multiple layers and for handling junction points
Algorithms and Bounds for Drawing Directed Graphs
In this paper we present a new approach to visualize directed graphs and
their hierarchies that completely departs from the classical four-phase
framework of Sugiyama and computes readable hierarchical visualizations that
contain the complete reachability information of a graph. Additionally, our
approach has the advantage that only the necessary edges are drawn in the
drawing, thus reducing the visual complexity of the resulting drawing.
Furthermore, most problems involved in our framework require only polynomial
time. Our framework offers a suite of solutions depending upon the
requirements, and it consists of only two steps: (a) the cycle removal step (if
the graph contains cycles) and (b) the channel decomposition and hierarchical
drawing step. Our framework does not introduce any dummy vertices and it keeps
the vertices of a channel vertically aligned. The time complexity of the main
drawing algorithms of our framework is , where is the number of
channels, typically much smaller than (the number of vertices).Comment: Appears in the Proceedings of the 26th International Symposium on
Graph Drawing and Network Visualization (GD 2018
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