17,044 research outputs found
Complexity Analysis of Balloon Drawing for Rooted Trees
In a balloon drawing of a tree, all the children under the same parent are
placed on the circumference of the circle centered at their parent, and the
radius of the circle centered at each node along any path from the root
reflects the number of descendants associated with the node. Among various
styles of tree drawings reported in the literature, the balloon drawing enjoys
a desirable feature of displaying tree structures in a rather balanced fashion.
For each internal node in a balloon drawing, the ray from the node to each of
its children divides the wedge accommodating the subtree rooted at the child
into two sub-wedges. Depending on whether the two sub-wedge angles are required
to be identical or not, a balloon drawing can further be divided into two
types: even sub-wedge and uneven sub-wedge types. In the most general case, for
any internal node in the tree there are two dimensions of freedom that affect
the quality of a balloon drawing: (1) altering the order in which the children
of the node appear in the drawing, and (2) for the subtree rooted at each child
of the node, flipping the two sub-wedges of the subtree. In this paper, we give
a comprehensive complexity analysis for optimizing balloon drawings of rooted
trees with respect to angular resolution, aspect ratio and standard deviation
of angles under various drawing cases depending on whether the tree is of even
or uneven sub-wedge type and whether (1) and (2) above are allowed. It turns
out that some are NP-complete while others can be solved in polynomial time. We
also derive approximation algorithms for those that are intractable in general
A Note on Plus-Contacts, Rectangular Duals, and Box-Orthogonal Drawings
A plus-contact representation of a planar graph is called -balanced if
for every plus shape , the number of other plus shapes incident to each
arm of is at most , where is the maximum degree
of . Although small values of have been achieved for a few subclasses of
planar graphs (e.g., - and -trees), it is unknown whether -balanced
representations with exist for arbitrary planar graphs.
In this paper we compute -balanced plus-contact representations for
all planar graphs that admit a rectangular dual. Our result implies that any
graph with a rectangular dual has a 1-bend box-orthogonal drawings such that
for each vertex , the box representing is a square of side length
.Comment: A poster related to this research appeared at the 25th International
Symposium on Graph Drawing & Network Visualization (GD 2017
Quad general tree drawing algorithm and general trees characterization: towards an environment for the experimental study on general tree drawing algorithms
Information visualization produces (interactive) visual representations of abstract data to reinforce human cognition and perception; thus enabling the viewer to gain knowledge about the internal structure of the data and causal relationships in it. The visualization of information hierarchies is concerned with the presentation of abstract hierarchical information about relationships between various entities. It has many applications in diverse domains such as software engineering, information systems, biology, and chemistry. Information hierarchies are typically modeled by an abstract tree, where vertices are entities and edges represent relationships between entities. The aim of visualizing tree drawings is to automatically produce drawings of trees which clearly reflect the relationships of the information hierarchy.
This thesis is primarily concerned with introducing the new general tree drawing algorithm Quad that produces good visually distinguishable angles, and a characterization of general trees which allows us to classify general trees into several types based on their characteristics. Both of these topics are part of building an experimental study environment for the evaluation of drawing algorithms for general trees.
The main achievements of this thesis include:
1. A study on characterization of general trees that aims to classify them into several types.
2. A tree drawing algorithm that produces visually distinguishable angles for high degree general trees with user specified angular coefficient
Interactive visualization of information hierarchies and applications on the web
The visualization of information hierarchies is concerned with the presentation of abstract hierarchical information about relationships between various entities. It has many applications in diverse domains such as software engineering, information systems, biology, and chemistry. Information hierarchies are typically modeled by an abstract tree, where vertices are entities and edges represent relationships between entities. The aim of visualizing tree drawings is to automatically produce drawings of trees which clearly reflect the relationships of the information hierarchy.
This thesis is primarily concerned with problems related to the automatic generation of area-efficient grid drawings of trees, interactively visualizing information hierarchies, and applying our techniques on Web data.
The main achievements of this thesis include:
1. An experimental study on algorithms that produce planar straight-line grid drawings of binary trees,
2. An experimental study that shows the algorithm for producing planar straight-line grid drawings of degree-d trees with n nodes with optimal linear area and with user-defined arbitrary aspect ratio, works well in practice,
3. A rings-based technique for interactively visualizing information hierarchies, in real-time,
4. A survey of Web visualization systems developed to address the lost in cyberspace problem,
5. A separation-based Web visualization system that we present as a viable solution to the lost in cyberspace problem,
6. A rings-based Web visualization system that we propose as a solution to the lost in cyberspace problem
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Recognizing Weighted Disk Contact Graphs
Disk contact representations realize graphs by mapping vertices bijectively
to interior-disjoint disks in the plane such that two disks touch each other if
and only if the corresponding vertices are adjacent in the graph. Deciding
whether a vertex-weighted planar graph can be realized such that the disks'
radii coincide with the vertex weights is known to be NP-hard. In this work, we
reduce the gap between hardness and tractability by analyzing the problem for
special graph classes. We show that it remains NP-hard for outerplanar graphs
with unit weights and for stars with arbitrary weights, strengthening the
previous hardness results. On the positive side, we present constructive
linear-time recognition algorithms for caterpillars with unit weights and for
embedded stars with arbitrary weights.Comment: 24 pages, 21 figures, extended version of a paper to appear at the
International Symposium on Graph Drawing and Network Visualization (GD) 201
Explorative Graph Visualization
Netzwerkstrukturen (Graphen) sind heutzutage weit verbreitet. Ihre Untersuchung dient dazu, ein besseres Verständnis ihrer Struktur und der durch sie modellierten realen Aspekte zu gewinnen. Die Exploration solcher Netzwerke wird zumeist mit Visualisierungstechniken unterstützt. Ziel dieser Arbeit ist es, einen Überblick über die Probleme dieser Visualisierungen zu geben und konkrete Lösungsansätze aufzuzeigen. Dabei werden neue Visualisierungstechniken eingeführt, um den Nutzen der geführten Diskussion für die explorative Graphvisualisierung am konkreten Beispiel zu belegen.Network structures (graphs) have become a natural part of everyday life and their analysis helps to gain an understanding of their inherent structure and the real-world aspects thereby expressed. The exploration of graphs is largely supported and driven by visual means. The aim of this thesis is to give a comprehensive view on the problems associated with these visual means and to detail concrete solution approaches for them. Concrete visualization techniques are introduced to underline the value of this comprehensive discussion for supporting explorative graph visualization
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