Tree maps are one of the widely used visualizations used for representing hierarchial data. One of the prominent examples are newsmap.jp. The paper does well in explaining the pros and cons of using a tree map. Tree maps may be one of the better ways of displaying hierarchial information in a more asthetical way, but they have their own limitations on space and representing additional data.
The article tries to compare a tree listing, venn diagram and a tree map based on an example on file listing. This example potrays one of the underlying strengths of a tree map which is showing size/ importance together with the necessary text. We can use the size, color and text to show these three dimensions. For the same data, a venn diagram would have taked much more space because it uses circular shapes. However a tree map loses its charm when there are too many blocks and it is difficult to grasp the relative importance using the area or color because the area would look similar or very small. In the newsmap.js example, if a particular news article is not all that important, it will be very difficult to show the headlines in the same area. Also since humans are not best at perceiving area as length or angle, comparing areas will be difficult.
The paper acknowledges some of these difficulties and gives a note on how tree maps can be used alternately. I think a better approach at visualizing a great amount of information is to split it in parts and let each part be seperately visualized by a tree map. From what I have read, I believe this paper is aiming to introduce tree map as a potential visualization and therefore there are not too many statistical references or examples.
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