Trees with Convex Faces and Optimal Angles

We consider drawings of trees in which all edges incident to leaves can be extended to infinite rays without crossing, partitioning the plane into infinite convex polygons. Among all such drawings we seek the one maximizing the angular resolution of the drawing. We find linear time algorithms for solving this problem, both for plane trees and for trees without a fixed embedding. In any such drawing, the edge lengths may be set independently of the angles, without crossing; we describe multiple strategies for setting these lengths.Comment: 12 pages, 10 figures. To appear at 14th Int. Symp. Graph Drawing, 200

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

Drawing Trees with Perfect Angular Resolution and Polynomial Area

We study methods for drawing trees with perfect angular resolution, i.e., with angles at each node v equal to 2{\pi}/d(v). We show: 1. Any unordered tree has a crossing-free straight-line drawing with perfect angular resolution and polynomial area. 2. There are ordered trees that require exponential area for any crossing-free straight-line drawing having perfect angular resolution. 3. Any ordered tree has a crossing-free Lombardi-style drawing (where each edge is represented by a circular arc) with perfect angular resolution and polynomial area. Thus, our results explore what is achievable with straight-line drawings and what more is achievable with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.Comment: 30 pages, 17 figure

Text and Spatial-Temporal Data Visualization

In this dissertation, we discuss a text visualization system, a tree drawing algorithm, a spatial-temporal data visualization paradigm and a tennis match visualization system. Corpus and corpus tools have become an important part of language teaching and learning. And yet text visualization is rarely used in this area. We present Text X-Ray, a Web tool for corpus-based language teaching and learning and the interactive text visualizations in Text X-Ray allow users to quickly examine a corpus or corpora at different levels of details: articles, paragraphs, sentences, and words. Level-based tree drawing is a common algorithm that produces intuitive and clear presentations of hierarchically structured information. However, new applications often introduces new aesthetic requirements that call for new tree drawing methods. We present an indented level-based tree drawing algorithm for visualizing parse trees of English language. This algorithm displays a tree with an aspect ratio that fits the aspect ratio of the newer computer displays, while presenting the words in a way that is easy to read. We discuss the design of the algorithm and its application in text visualization for linguistic analysis and language learning. A story is a chain of events. Each event has multiple dimensions, including time, location, characters, actions, and context. Storyline visualizations attempt to visually present the many dimensions of a story’s events and their relationships. Integrating the temporal and spatial dimension in a single visualization view is often desirable but highly challenging. One of the main reasons is that spatial data is inherently 2D while temporal data is inherently 1D. We present a storyline visualization technique that integrate both time and location information in a single view. Sports data visualization can be a useful tool for analyzing or presenting sports data. We present a new technique for visualizing tennis match data. It is designed as a supplement to online live streaming or live blogging of tennis matches and can retrieve data directly from a tennis match live blogging web site and display 2D interactive view of match statistics. Therefore, it can be easily integrated with the current live blogging platforms used by many news organizations. The visualization addresses the limitations of the current live coverage of tennis matches by providing a quick overview and also a great amount of details on demand

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