19 research outputs found
Are crossings important for drawing large graphs?
Reducing the number of edge crossings is considered one of the most important graph drawing aesthetics. While real-world graphs tend to be large and dense, most of the earlier work on evaluating the impact of edge crossings utilizes relatively small graphs that are manually generated and manipulated. We study the effect on task performance of increased edge crossings in automatically generated layouts for graphs, from different datasets, with different sizes, and with different densities. The results indicate that increasing the number of crossings negatively impacts accuracy and performance time and that impact is significant for small graphs but not significant for large graphs. We also quantitatively evaluate the impact of edge crossings on crossing angles and stress in automatically constructed graph layouts. We find a moderate correlation between minimizing stress and the minimizing the number of crossings. © Springer-Verlag Berlin Heidelberg 2014.National Science Foundation, NSF: CCF-1115971National Science Foundation, NSF: DEB-105357
Compact Drawings of 1-Planar Graphs with Right-Angle Crossings and Few Bends
We study the following classes of beyond-planar graphs: 1-planar, IC-planar,
and NIC-planar graphs. These are the graphs that admit a 1-planar, IC-planar,
and NIC-planar drawing, respectively. A drawing of a graph is 1-planar if every
edge is crossed at most once. A 1-planar drawing is IC-planar if no two pairs
of crossing edges share a vertex. A 1-planar drawing is NIC-planar if no two
pairs of crossing edges share two vertices. We study the relations of these
beyond-planar graph classes (beyond-planar graphs is a collective term for the
primary attempts to generalize the planar graphs) to right-angle crossing (RAC)
graphs that admit compact drawings on the grid with few bends. We present four
drawing algorithms that preserve the given embeddings. First, we show that
every -vertex NIC-planar graph admits a NIC-planar RAC drawing with at most
one bend per edge on a grid of size . Then, we show that
every -vertex 1-planar graph admits a 1-planar RAC drawing with at most two
bends per edge on a grid of size . Finally, we make two
known algorithms embedding-preserving; for drawing 1-planar RAC graphs with at
most one bend per edge and for drawing IC-planar RAC graphs straight-line
Recognizing and Drawing IC-planar Graphs
IC-planar graphs are those graphs that admit a drawing where no two crossed
edges share an end-vertex and each edge is crossed at most once. They are a
proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph
with vertices, we present an -time algorithm that computes a
straight-line drawing of in quadratic area, and an -time algorithm
that computes a straight-line drawing of with right-angle crossings in
exponential area. Both these area requirements are worst-case optimal. We also
show that it is NP-complete to test IC-planarity both in the general case and
in the case in which a rotation system is fixed for the input graph.
Furthermore, we describe a polynomial-time algorithm to test whether a set of
matching edges can be added to a triangulated planar graph such that the
resulting graph is IC-planar
Graph Drawing via Gradient Descent,
Readability criteria, such as distance or neighborhood preservation, are
often used to optimize node-link representations of graphs to enable the
comprehension of the underlying data. With few exceptions, graph drawing
algorithms typically optimize one such criterion, usually at the expense of
others. We propose a layout approach, Graph Drawing via Gradient Descent,
, that can handle multiple readability criteria. can optimize
any criterion that can be described by a smooth function. If the criterion
cannot be captured by a smooth function, a non-smooth function for the
criterion is combined with another smooth function, or auto-differentiation
tools are used for the optimization. Our approach is flexible and can be used
to optimize several criteria that have already been considered earlier (e.g.,
obtaining ideal edge lengths, stress, neighborhood preservation) as well as
other criteria which have not yet been explicitly optimized in such fashion
(e.g., vertex resolution, angular resolution, aspect ratio). We provide
quantitative and qualitative evidence of the effectiveness of with
experimental data and a functional prototype:
\url{http://hdc.cs.arizona.edu/~mwli/graph-drawing/}.Comment: Appears in the Proceedings of the 28th International Symposium on
Graph Drawing and Network Visualization (GD 2020