Fast Algorithms for Constructing Maximum Entropy Summary Trees

Karloff? and Shirley recently proposed summary trees as a new way to visualize large rooted trees (Eurovis 2013) and gave algorithms for generating a maximum-entropy k-node summary tree of an input n-node rooted tree. However, the algorithm generating optimal summary trees was only pseudo-polynomial (and worked only for integral weights); the authors left open existence of a olynomial-time algorithm. In addition, the authors provided an additive approximation algorithm and a greedy heuristic, both working on real weights. This paper shows how to construct maximum entropy k-node summary trees in time O(k^2 n + n log n) for real weights (indeed, as small as the time bound for the greedy heuristic given previously); how to speed up the approximation algorithm so that it runs in time O(n + (k^4/eps?) log(k/eps?)), and how to speed up the greedy algorithm so as to run in time O(kn + n log n). Altogether, these results make summary trees a much more practical tool than before.Comment: 17 pages, 4 figures. Extended version of paper appearing in ICALP 201

A Pattern Approach to Examine the Design Space of Spatiotemporal Visualization

Pattern language has been widely used in the development of visualization systems. This dissertation applies a pattern language approach to explore the design space of spatiotemporal visualization. The study provides a framework for both designers and novices to communicate, develop, evaluate, and share spatiotemporal visualization design on an abstract level. The touchstone of the work is a pattern language consisting of fifteen design patterns and four categories. In order to validate the design patterns, the researcher created two visualization systems with this framework in mind. The first system displayed the daily routine of human beings via a polygon-based visualization. The second system showed the spatiotemporal patterns of co-occurring hashtags with a spiral map, sunburst diagram, and small multiples. The evaluation results demonstrated the effectiveness of the proposed design patterns to guide design thinking and create novel visualization practices

Scalable, Robust Visualization of Very Large Trees

The TreeJuxtaposer system [MGT ∗ 03] allowed visual comparison of large trees with guaranteed visibility of landmarks and Focus+Context navigation. While that system allowed exploration and comparison of larger datasets than previous work, it was limited to a single tree of 775,000 nodes by a large memory footprint. In this paper, we describe the theoretical limitations to TreeJuxtaposer’s architecture that severely restrict its scalability. We provide two scalable, robust solutions to these limitations: TJC and TJC-Q. TJC is a system that supports browsing trees up to 15 million nodes by exploiting leading-edge graphics hardware while TJC-Q allows browsing trees up to 5 million nodes on commodity platforms. Both of these systems use a fast new algorithm for drawing and culling and benefit from a complete redesign of all data structures for more efficient memory usage and reduced preprocessing time. Categories and Subject Descriptors (according to ACM CCS): I.3.6 [Computer Graphics]: Graphics data structures and data type