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

RELT - Visualizing trees on mobile devices

The small screens on increasingly used mobile devices challenge the traditional visualization methods designed for desktops. This paper presents a method called "Radial Edgeless Tree" (RELT) for visualizing trees in a 2-dimensional space. It combines the existing connection tree drawing with the space-filling approach to achieve the efficient display of trees in a small geometrical area, such as the screen that are commonly used in mobile devices. We recursively calculate a set of non-overlapped polygonal nodes that are adjacent in the hierarchical manner. Thus, the display space is fully used for displaying nodes, while the hierarchical relationships among the nodes are presented by the adjacency (or boundary-sharing) of the nodes. It is different from the other traditional connection approaches that use a node-link diagram to present the parent-child relationships which waste the display space. The hierarchy spreads from north-west to south-east in a top-down manner which naturally follows the traditional way of human perception of hierarchies. We discuss the characteristics, advantages and limitations of this new technique and suggestions for future research. © Springer-Verlag Berlin Heidelberg 2007

An Iterative and Toolchain-Based Approach to Automate Scanning and Mapping Computer Networks

As today's organizational computer networks are ever evolving and becoming more and more complex, finding potential vulnerabilities and conducting security audits has become a crucial element in securing these networks. The first step in auditing a network is reconnaissance by mapping it to get a comprehensive overview over its structure. The growing complexity, however, makes this task increasingly effortful, even more as mapping (instead of plain scanning), presently, still involves a lot of manual work. Therefore, the concept proposed in this paper automates the scanning and mapping of unknown and non-cooperative computer networks in order to find security weaknesses or verify access controls. It further helps to conduct audits by allowing comparing documented with actual networks and finding unauthorized network devices, as well as evaluating access control methods by conducting delta scans. It uses a novel approach of augmenting data from iteratively chained existing scanning tools with context, using genuine analytics modules to allow assessing a network's topology instead of just generating a list of scanned devices. It further contains a visualization model that provides a clear, lucid topology map and a special graph for comparative analysis. The goal is to provide maximum insight with a minimum of a priori knowledge.Comment: 7 pages, 6 figure

Seeking Bob Thompson : dialogue/object.

This thesis documents the research, development, and implementation of the exhibition Seeking Bob Thompson. The exhibition portion of this curatorial project was completed in the fall of 2012 using work in the Hite Art Institute collection as well as works borrowed from commercial galleries, art centers, and private collections throughout the United States. Intended to re-expose and reveal the well-known but little exhibited in his hometown, Louisville artist, Bob Thompson, the project focused on delineating reoccurring themes in Thompson\u27s oeuvre that were pertinent to his own process of establishing and defining his artistic identity with particular attention to his appropriations of Old Master compositions. The exhibition provided the opportunity to make use of the university\u27s archive on Thompson, the university\u27s art collection, and its other resources and to extend access to these resources to the region. The exhibition fulfilled the three primary missions of the Hite Galleries: to showcase the artworks of university students and faculty, to present the university\u27s art collection to the wider public, and to provide an exposure of significant art to the university\u27s students and the local community. Both the written and visual components of this thesis project express a view of Thompson as driven by his pursuit and expression of his sense of freedom and his commitment to art history

Visualization of graphs and trees for software analysis

A software architecture is an abstraction of a software system, which is indispensable for many software engineering tasks. Unfortunately, in many cases information pertaining to the software architecture is not available, outdated, or inappropriate for the task at hand. The RECONSTRUCTOR project focuses on software architecture reconstruction, i.e., obtaining architectural information from an existing system. Our research, which is part of RECONSTRUCTOR, focuses on interactive visualization and tries to answer the following question: How can users be enabled to understand the large amounts of information relevant for program understanding using visual representations? To answer this question, we have iteratively developed a number of techniques for visualizing software systems. A large number of these cases consists of hierarchically organized data, combined with adjacency relations. Examples are function calls within a hierarchically organized software system and correspondence relations between two different versions of a hierarchically organized software system. Hierarchical Edge Bundles (HEBs) are used to visualize adjacency relations in hierarchically organized data, such as the aforementioned function calls within a software system. HEBs significantly reduce visual clutter by visually bundling relations together. Massive Sequence Views (MSVs) are used in conjunction with HEBs to enable analysis of sequences of relations, such as function-call traces. HEBs are furthermore used to visually compare hierarchically organized data, e.g., two different versions of a software system. HEBs visually emphasize splits, joins, and relocations of subhierarchies and provide for interactive selection of sets of relations. Since HEBs require a hierarchy to perform the bundling, we present Force-Directed Edge Bundles (FDEBs) as an alternative to visually bundle relations together in the absence of a hierarchical component. FDEBs use a self-organizing approach to bundling in which edges are modeled as flexible springs that can attract each other. As a result, visual clutter is reduced and high-level edge patterns are better visible. Finally, in all these methods, a clear depiction of the direction of edges is important. We have therefore performed a separate study in which we evaluated ten representations (including the standard arrow) for depicting directed edges in a controlled user study

Enabling effective tree exploration using visual cues

© 2018 Elsevier Ltd This article presents a new interactive visualization for exploring large hierarchical structures by providing visual cues on a node link tree visualization. Our technique provides topological previews of hidden substructures with three types of visual cues including simple cues, tree cues and treemap cues. We demonstrate the visual cues on Degree-of-Interest Tree (DOITree) due to its familiar mapping, its capability of providing multiple focused nodes, and its dynamic rescaling of substructures to fit the available space. We conducted a usability study with 28 participants that measured completion time and accuracy across five different topology search tasks. The simple cues had the fastest completion time across three of the node identification tasks. The treemap cues had the highest rate of correct answers on four of the five tasks, although only reaching statistical significance for two of these. As predicted, user ratings demonstrated a preference for the easy to understand tree cues followed by the simple cue, despite this not consistently reflected in performance results

Efficient abstractions for visualization and interaction

Abstractions, such as functions and methods, are an essential tool for any programmer. Abstractions encapsulate the details of a computation: the programmer only needs to know what the abstraction achieves, not how it achieves it. However, using abstractions can come at a cost: the resulting program may be inefficient. This can lead to programmers not using some abstractions, instead writing the entire functionality from the ground up. In this thesis, we present several results that make this situation less likely when programming interactive visualizations. We present results that make abstractions more efficient in the areas of graphics, layout and events

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

The Coral of Life

The Tree of Life (ToL) has been of central importance in the biological sciences, usually understood as a model or a metaphor, and portrayed in various graphical forms to summarize the history of life as a single diagram. If it is seen as a mathematical construct—a rooted graph theoretical tree or, as more recently viewed, a directed network [Network of Life (NoL)]—then its proper visualization is not feasible, for both epistemological and technical reasons. As an overview included in this study demonstrates, published ToLs and NoLs are extremely diverse in appearance and content, and they suffer from inevitable bias towards particular groups, or are restricted to a single major taxon. Metaphorical trees are even less useful for the purpose, because ramification is the only property of botanical trees that may be interpreted in an evolutionary or phylogenetic context. This paper argues that corals, as suggested by Darwin in his early notebooks, are superior to trees as metaphors, and may also be used as mathematical models. A coral diagram is useful for portraying past and present life because it is suitable: (1) to illustrate bifurcations and anastomoses, (2) to depict species richness of taxa proportionately, (3) to show chronology, extinct taxa and major evolutionary innovations, (4) to express taxonomic continuity, (5) to expand particulars due to its self-similarity, and (6) to accommodate a genealogy-based, rank-free classification. This paper is supplemented with a figure, The Coral of Life (CoL), which is, to the author’s knowledge, the first attempt to combine all of the above features in a single diagram for the entirety of life, thus serving as a prototype for further analysis and improvement. The discussion is partly historical: references to classical and modern writings help the reader to understand how biological thinking and methods of visualization have evolved to reach this achievement