Capturing the Design Space of Sequential Space-Filling Layouts Thomas Baudel and Bertjan Broeksema (a) (b) (c) (d) Order: data Size: data.Population Chunking: BestMinAspectRatio Recurse: #items > 2 Phrase: ZigZag Order: data.Population Size: data.Population Chunking: BestMinAspectRatio Recurse: never Phrase: Spiral Order: data Size: data.Population Chunking: PivotBySize Recurse: #items > 2 Phrase: WorstDiscontinuous Order: data Size: constant Chunking: HalfItemCount Recurse: #items %4 == 0 Phrase: Hilbert Fig. 1. various space-filling layout examples: (a) strip (with recursion), (b) spiral, (c) pivot by middle. (d) hilbert phrasing, Chunks are separated by black lines, individual items by red lines. Abstract—We characterize the design space of the algorithms that sequentially tile a rectangular area with smaller, fixed-surface, rectangles. This space consist of five independent dimensions: Order, Size, Score, Recurse and Phrase. Each of these dimensions describe a particular aspect of such layout tasks. This class of layouts is interesting, because, beyond encompassing simple grids, tables and trees, it also includes all kinds of treemaps involving the placement of rectangles. For instance, Slice and dice, Squarified, Strip and Pivot layouts are various points in this five dimensional space. Many classic statistics visualizations, such as 100% stacked bar charts, mosaic plots and dimensional stacking, are also instances of this class. A few new and potentially interesting points in this space are introduced, such as spiral treemaps and variations on the strip layout. The core algorithm is implemented as a JavaScript prototype that can be used as a layout component in a variety of InfoViz toolkits. Index Terms—Layout, visualization models, tables & tree layouts, grids, treemaps (slice and dice, strip, squarified and pivot varia- tions), mosaic plots, dimensional stacking. 1 I NTRODUCTION Treemaps are now over twenty years old [14]. This visualization tech- nique has generated much enthusiasm in the information visualization community and has become a small research area of its own [21]. In the general public, treemaps have had their moments of fame with the map of the market [23], and are slowly making their way as a standard device in the toolkit of graphic designers [4, 24]. Yet, for a technology about as old as the World WideWeb, which keeps a high level of interest in the research community, we could hope for more salient success: treemaps and related rectangular space- filling approaches are still not a common visualization device of every- day use. Success stories for treemaps are the result of talented graphic design work, where the visualization designer has crafted the layout and visualization parameters to match a specific context and narrative. We attribute the need for careful crafting to the lack of a good un- derstanding of their design space. Choosing the right layout parame- • Thomas Baudel is with IBM ILOG Advanced Studies. E-mail: baudelth@fr.ibm.com. • Bertjan Broeksema is with IBM ILOG Advanced Studies,Institute Johann Bernoulli, Univ. of Groningen, The Netherlands and INRIA, Bordeaux, France. E-mail:bertjan.broeksema@fr.ibm.com. Manuscript received 31 March 2012; accepted 1 August 2012; posted online 14 October 2012; mailed on 5 October 2012. For information on obtaining reprints of this article, please send e-mail to: tvcg@computer.org. ters to suit a particular dataset and features to be highlighted requires a solid experience and a dedicated presentation effort. In analysis con- texts, this presentation effort is a distraction from the research task and therefore often sub-optimal layouts are used. This lack of presen- tation automation, or easier customizability, creates a barrier to more widespread adoption in the contexts where rectangular space-filling layouts, such as treemaps, could really bring insight. Our goal here is to define more precisely the design space of a par- ticular class of layout algorithms that lie at the root of the treemap con- cept: rectangular space-filling layouts, i.e. the layouts that tile a unit square with rectangles in a space-filling manner. We describe how in- put data is transformed into a set of rectangles that tile the unit square through a process that is constrained by the dimensions that span this design space. In addition we contribute a universal algorithm for some class of rectangular space-filling layouts. This universal algorithm is parametrized by functors that represent the described dimensions. We present the algorithm with various examples of useful values for these dimensions, which allow creating well known as well as novel rectan- gular, space-filling layouts. We believe that a solid understanding of this design space can serve as a basis to develop methods and heuris- tics that determine the most appropriate layout given a particular data set. Finally, it has been suggested that the design-space of space-filling rectangular layouts is very large and that the generic problem of creat- ing such layouts fall in the category of NP-hard problems [8]. To the contrary, we show here that: 1. Useful rectangular space-filling layouts belong to a class of lim- ited complexity, which we call sequential space-filling layouts. 2593 1077-2626/12/$31.00 © 2012 IEEE Published by the IEEE Computer Society IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 18, NO. 12, DECEMBER 2012