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

Proximity Drawings of High-Degree Trees

A drawing of a given (abstract) tree that is a minimum spanning tree of the vertex set is considered aesthetically pleasing. However, such a drawing can only exist if the tree has maximum degree at most 6. What can be said for trees of higher degree? We approach this question by supposing that a partition or covering of the tree by subtrees of bounded degree is given. Then we show that if the partition or covering satisfies some natural properties, then there is a drawing of the entire tree such that each of the given subtrees is drawn as a minimum spanning tree of its vertex set

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

The Partial Visibility Representation Extension Problem

For a graph $G$, a function $\psi$ is called a \emph{bar visibility representation} of $G$ when for each vertex $v \in V(G)$, $\psi(v)$ is a horizontal line segment (\emph{bar}) and $uv \in E(G)$ iff there is an unobstructed, vertical, $\varepsilon$-wide line of sight between $\psi(u)$ and $\psi(v)$. Graphs admitting such representations are well understood (via simple characterizations) and recognizable in linear time. For a directed graph $G$, a bar visibility representation $\psi$ of $G$, additionally, puts the bar $\psi(u)$ strictly below the bar $\psi(v)$ for each directed edge $(u,v)$ of $G$. We study a generalization of the recognition problem where a function $\psi'$ defined on a subset $V'$ of $V(G)$ is given and the question is whether there is a bar visibility representation $\psi$ of $G$ with $\psi(v) = \psi'(v)$ for every $v \in V'$. We show that for undirected graphs this problem together with closely related problems are \NP-complete, but for certain cases involving directed graphs it is solvable in polynomial time.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Queue Layout of Planar 3−Tree

Graph drawing is essential for data representation. This thesis addresses various graph drawing techniques, their implementation, and enhancements. First, we discuss the 3D grid drawing techniques. The subsequent chapters address the Stack Layout and Queue layout of the graph. The application of Stack and Queue layout and its importance also discussed. Section 4, dedicated to outerplanar Graph. In this chapter, we have discussed how outerplanar Graphs are implemented and their queue and track layouts. The most important part of this thesis is chapter 5, in which the implementation of planar 3-Tree is given. An outerPlanar graph and Planar 3-Tree are internally related. The known upper bound of the queue number of planar 3-Tree is 7. We have implemented the queue layout of 2-Layer planar 3-Tree using two queues and then generalized this experiment for any arbitrary number of levels

A combinatorial approach to orthogonal placement problems

liegt nicht vor!Wir betrachten zwei Familien von NP-schwierigen orthogonalen Platzierungsproblemen aus dem Bereich der Informationsvisualisierung von einem theoretischen und praktischen Standpunkt aus. Diese Arbeit enthält ein gemeinsames kombinatorisches Gerüst für Kompaktierungsprobleme aus dem Bereich des orthogonalen Graphenzeichnens und Beschriftungsprobleme von Punktmengen aus dem Gebiet der Computer-Kartografie. Bei den Kompaktierungsproblemen geht es darum, eine gegebene dimensionslose Beschreibung der orthogonalen Form eines Graphen in eine orthogonale Gitterzeichnung mit kurzen Kanten und geringem Flächenverbrauch zu transformieren. Die Beschriftungsprobleme haben zur Aufgabe, eine gegebene Menge von rechteckigen Labels so zu platzieren, dass eine lesbare Karte entsteht. In einer klassischen Anwendung repräsentieren die Punkte beispielsweise Städte einer Landkarte, und die Labels enthalten die Namen der Städte. Wir präsentieren neue kombinatorische Formulierungen für diese Probleme und verwenden dabei eine pfad- und kreisbasierte graphentheoretische Eigenschaft in einem zugehörigen problemspezifschen Paar von Constraint-Graphen. Die Umformulierung ermöglicht es uns, exakte Algorithmen für die Originalprobleme zu entwickeln. Umfassende experimentelle Studien mit Benchmark-Instanzen aus der Praxis zeigen, dass unsere Algorithmen, die auf linearer Programmierung beruhen, in der Lage sind, große Instanzen der Platzierungsprobleme beweisbar optimal und in kurzer Rechenzeit zu lösen. Ferner kombinieren wir die Formulierungen für Kompaktierungs- und Beschriftungsprobleme und präsentieren einen exakten algorithmischen Ansatz für ein Graphbeschriftungsproblem. Oftmals sind unsere neuen Algorithmen die ersten exakten Algorithmen für die jeweilige Problemvariante

A combinatorial approach to orthogonal placement problems

liegt nicht vor!Wir betrachten zwei Familien von NP-schwierigen orthogonalen Platzierungsproblemen aus dem Bereich der Informationsvisualisierung von einem theoretischen und praktischen Standpunkt aus. Diese Arbeit enthält ein gemeinsames kombinatorisches Gerüst für Kompaktierungsprobleme aus dem Bereich des orthogonalen Graphenzeichnens und Beschriftungsprobleme von Punktmengen aus dem Gebiet der Computer-Kartografie. Bei den Kompaktierungsproblemen geht es darum, eine gegebene dimensionslose Beschreibung der orthogonalen Form eines Graphen in eine orthogonale Gitterzeichnung mit kurzen Kanten und geringem Flächenverbrauch zu transformieren. Die Beschriftungsprobleme haben zur Aufgabe, eine gegebene Menge von rechteckigen Labels so zu platzieren, dass eine lesbare Karte entsteht. In einer klassischen Anwendung repräsentieren die Punkte beispielsweise Städte einer Landkarte, und die Labels enthalten die Namen der Städte. Wir präsentieren neue kombinatorische Formulierungen für diese Probleme und verwenden dabei eine pfad- und kreisbasierte graphentheoretische Eigenschaft in einem zugehörigen problemspezifschen Paar von Constraint-Graphen. Die Umformulierung ermöglicht es uns, exakte Algorithmen für die Originalprobleme zu entwickeln. Umfassende experimentelle Studien mit Benchmark-Instanzen aus der Praxis zeigen, dass unsere Algorithmen, die auf linearer Programmierung beruhen, in der Lage sind, große Instanzen der Platzierungsprobleme beweisbar optimal und in kurzer Rechenzeit zu lösen. Ferner kombinieren wir die Formulierungen für Kompaktierungs- und Beschriftungsprobleme und präsentieren einen exakten algorithmischen Ansatz für ein Graphbeschriftungsproblem. Oftmals sind unsere neuen Algorithmen die ersten exakten Algorithmen für die jeweilige Problemvariante

Area-Efficient Drawings of Outer-1-Planar Graphs

We study area-efficient drawings of planar graphs: embeddings of graphs on an integer grid so that the bounding box of the drawing is minimized. Our focus is on the class of outer-1-planar graphs: the family of planar graphs that can be drawn on the plane with all vertices on the outer-face so that each edge is crossed at most once. We first present two straight-line drawing algorithms that yield small-area straight-line drawings for the subclass of complete outer-1-planar graphs. Further, we give an algorithm that produces an orthogonal drawing of any outer-1-plane graph in O(n log n) area while keeping the number of bends per edge relatively small