Treemaps, a space-filling method for visualizing large hierarchical data sets, are receiving increasing attention. Several algorithms have been previously proposed to create more useful displays by controlling the aspect ratios of the rectangles that make up a treemap. While these algorithms do improve visibility of small items in a single layout, they introduce instability over time in the display of dynamically changing data, fail to preserve 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 paper introduces a new "strip" treemap algorithm which addresses these shortcomings, and analyzes other "pivot" algorithms we recently developed showing the trade-offs between them. These ordered treemap algorithms ensure that items near each other in the given order will be near each other in the treemap layout. Using experimental evidence from Monte Carlo trials and from actual stock market data, we show that, compared to other layout algorithms, ordered treemaps are more stable, while maintaining relatively favorable aspect ratios of the constituent rectangles. A user study with 20 participants clarifies the human performance benefits of the new algorithms. Finally, we present quantum treemap algorithms, which modify the layout of the continuous treemap algorithms to generate rectangles that are integral multiples of an input object size. The quantum treemap algorithm has been applied to PhotoMesa, an application that supports browsing of large numbers of images.
