28 research outputs found
Drawing Big Graphs using Spectral Sparsification
Spectral sparsification is a general technique developed by Spielman et al.
to reduce the number of edges in a graph while retaining its structural
properties. We investigate the use of spectral sparsification to produce good
visual representations of big graphs. We evaluate spectral sparsification
approaches on real-world and synthetic graphs. We show that spectral
sparsifiers are more effective than random edge sampling. Our results lead to
guidelines for using spectral sparsification in big graph visualization.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
3D Visibility Representations of 1-planar Graphs
We prove that every 1-planar graph G has a z-parallel visibility
representation, i.e., a 3D visibility representation in which the vertices are
isothetic disjoint rectangles parallel to the xy-plane, and the edges are
unobstructed z-parallel visibilities between pairs of rectangles. In addition,
the constructed representation is such that there is a plane that intersects
all the rectangles, and this intersection defines a bar 1-visibility
representation of G.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Planar L-Drawings of Directed Graphs
We study planar drawings of directed graphs in the L-drawing standard. We
provide necessary conditions for the existence of these drawings and show that
testing for the existence of a planar L-drawing is an NP-complete problem.
Motivated by this result, we focus on upward-planar L-drawings. We show that
directed st-graphs admitting an upward- (resp. upward-rightward-) planar
L-drawing are exactly those admitting a bitonic (resp. monotonically
increasing) st-ordering. We give a linear-time algorithm that computes a
bitonic (resp. monotonically increasing) st-ordering of a planar st-graph or
reports that there exists none.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
On Smooth Orthogonal and Octilinear Drawings: Relations, Complexity and Kandinsky Drawings
We study two variants of the well-known orthogonal drawing model: (i) the
smooth orthogonal, and (ii) the octilinear. Both models form an extension of
the orthogonal, by supporting one additional type of edge segments (circular
arcs and diagonal segments, respectively).
For planar graphs of max-degree 4, we analyze relationships between the graph
classes that can be drawn bendless in the two models and we also prove
NP-hardness for a restricted version of the bendless drawing problem for both
models. For planar graphs of higher degree, we present an algorithm that
produces bi-monotone smooth orthogonal drawings with at most two segments per
edge, which also guarantees a linear number of edges with exactly one segment.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
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
Visualizing Co-Phylogenetic Reconciliations
We introduce a hybrid metaphor for the visualization of the reconciliations
of co-phylogenetic trees, that are mappings among the nodes of two trees. The
typical application is the visualization of the co-evolution of hosts and
parasites in biology. Our strategy combines a space-filling and a node-link
approach. Differently from traditional methods, it guarantees an unambiguous
and `downward' representation whenever the reconciliation is time-consistent
(i.e., meaningful). We address the problem of the minimization of the number of
crossings in the representation, by giving a characterization of planar
instances and by establishing the complexity of the problem. Finally, we
propose heuristics for computing representations with few crossings.Comment: This paper appears in the Proceedings of the 25th International
Symposium on Graph Drawing and Network Visualization (GD 2017
GiViP: A Visual Profiler for Distributed Graph Processing Systems
Analyzing large-scale graphs provides valuable insights in different
application scenarios. While many graph processing systems working on top of
distributed infrastructures have been proposed to deal with big graphs, the
tasks of profiling and debugging their massive computations remain time
consuming and error-prone. This paper presents GiViP, a visual profiler for
distributed graph processing systems based on a Pregel-like computation model.
GiViP captures the huge amount of messages exchanged throughout a computation
and provides an interactive user interface for the visual analysis of the
collected data. We show how to take advantage of GiViP to detect anomalies
related to the computation and to the infrastructure, such as slow computing
units and anomalous message patterns.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
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
Reconstructing Generalized Staircase Polygons with Uniform Step Length
Visibility graph reconstruction, which asks us to construct a polygon that
has a given visibility graph, is a fundamental problem with unknown complexity
(although visibility graph recognition is known to be in PSPACE). We show that
two classes of uniform step length polygons can be reconstructed efficiently by
finding and removing rectangles formed between consecutive convex boundary
vertices called tabs. In particular, we give an -time reconstruction
algorithm for orthogonally convex polygons, where and are the number of
vertices and edges in the visibility graph, respectively. We further show that
reconstructing a monotone chain of staircases (a histogram) is fixed-parameter
tractable, when parameterized on the number of tabs, and polynomially solvable
in time under reasonable alignment restrictions.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Experimental Evaluation of Book Drawing Algorithms
A -page book drawing of a graph consists of a linear ordering of
its vertices along a spine and an assignment of each edge to one of the
pages, which are half-planes bounded by the spine. In a book drawing, two edges
cross if and only if they are assigned to the same page and their vertices
alternate along the spine. Crossing minimization in a -page book drawing is
NP-hard, yet book drawings have multiple applications in visualization and
beyond. Therefore several heuristic book drawing algorithms exist, but there is
no broader comparative study on their relative performance. In this paper, we
propose a comprehensive benchmark set of challenging graph classes for book
drawing algorithms and provide an extensive experimental study of the
performance of existing book drawing algorithms.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017