Ordered and Quantum Treemaps: Making Effective Use of 2D Space to Display Hierarchies

Abstract

Treemaps are a space-filling visualization method capable of representing the large hierarchical collections of quantitative data in a compact display. A treemap works by dividing the display area into a nested sequence of rectangles, whose areas correspond to an attribute of the data set by effectively combining the aspects of a Venn diagram and a pie chart. Several algorithms are available to create more useful displays by controlling the aspect ratios of the rectangles that make up a treemap. While these algorithms do improve the visibility of small items in a single layout, they introduce instability over time in the display of dynamically changing data, fail to preserve the order of the underlying data, and create layouts that are difficult to visually search. In addition, continuous treemap algorithms are not suitable for displaying fixed-sized objects within them, such as images. This chapter introduces a new “strip” treemap algorithm, which addresses these shortcomings. The chapter analyzes other pivot algorithms developed recently and shows the trade-offs between the strip algorithm and these algorithms. Using experimental evidences from the Monte Carlo trials and from the actual stock market data, it is found that ordered treemaps are more stable as compared to other layouts, while maintaining relatively favorable aspect ratios of the constituent rectangles. The chapter also discusses the quantum treemap algorithms, which modify the layout of the continuous treemap algorithms to generate rectangles that are the integral multiples of an input object size. The quantum treemap algorithm has been applied to PhotoMesa, an application that supports the browsing of large numbers of images.