37,849 research outputs found
Analogies between the crossing number and the tangle crossing number
Tanglegrams are special graphs that consist of a pair of rooted binary trees
with the same number of leaves, and a perfect matching between the two
leaf-sets. These objects are of use in phylogenetics and are represented with
straightline drawings where the leaves of the two plane binary trees are on two
parallel lines and only the matching edges can cross. The tangle crossing
number of a tanglegram is the minimum crossing number over all such drawings
and is related to biologically relevant quantities, such as the number of times
a parasite switched hosts.
Our main results for tanglegrams which parallel known theorems for crossing
numbers are as follows. The removal of a single matching edge in a tanglegram
with leaves decreases the tangle crossing number by at most , and this
is sharp. Additionally, if is the maximum tangle crossing number of
a tanglegram with leaves, we prove
. Further,
we provide an algorithm for computing non-trivial lower bounds on the tangle
crossing number in time. This lower bound may be tight, even for
tanglegrams with tangle crossing number .Comment: 13 pages, 6 figure
A parent-centered radial layout algorithm for interactive graph visualization and animation
We have developed (1) a graph visualization system that allows users to
explore graphs by viewing them as a succession of spanning trees selected
interactively, (2) a radial graph layout algorithm, and (3) an animation
algorithm that generates meaningful visualizations and smooth transitions
between graphs while minimizing edge crossings during transitions and in static
layouts.
Our system is similar to the radial layout system of Yee et al. (2001), but
differs primarily in that each node is positioned on a coordinate system
centered on its own parent rather than on a single coordinate system for all
nodes. Our system is thus easy to define recursively and lends itself to
parallelization. It also guarantees that layouts have many nice properties,
such as: it guarantees certain edges never cross during an animation.
We compared the layouts and transitions produced by our algorithms to those
produced by Yee et al. Results from several experiments indicate that our
system produces fewer edge crossings during transitions between graph drawings,
and that the transitions more often involve changes in local scaling rather
than structure.
These findings suggest the system has promise as an interactive graph
exploration tool in a variety of settings
Experimental analysis of the accessibility of drawings with few segments
The visual complexity of a graph drawing is defined as the number of
geometric objects needed to represent all its edges. In particular, one object
may represent multiple edges, e.g., one needs only one line segment to draw two
collinear incident edges. We study the question if drawings with few segments
have a better aesthetic appeal and help the user to asses the underlying graph.
We design an experiment that investigates two different graph types (trees and
sparse graphs), three different layout algorithms for trees, and two different
layout algorithms for sparse graphs. We asked the users to give an aesthetic
ranking on the layouts and to perform a furthest-pair or shortest-path task on
the drawings.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
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