Circular Drawings of Rooted Trees

We describe an algorithm producing circular l a y outs for trees, that is drawings, where subtrees of a node lie within circles, and these circles are themselves placed on the circumference of a circle. The complexity and methodology of our algorithm compares to Reingold and Tilford's algorithm for trees [11]. Moreover, the algorithm naturally admits distortion transformations of the layout. This, added to its low complexity, makes it very well suited to be used in an interactive environment. 1. INTRODUCTION Rooted trees are at the center of many problems and applications in computer science. Information systems, multimedia documents databases, or virtual reality scene descriptions are only a few examples in which they are used. Their widespread use is most probably the result of the fact that they capture and reflect the way humans often organize information. A visual representation of these structures is often a major tool to help the user finding his/her way in exploring data; hence the importance of graph drawing and exploration in information visualization. Methods for drawing trees has received a significant attention for a long time and it still reappears as an intermediate task in many applications. The classic algorithm by Reingold and Tilford [11], improved later in [14], gives a very effective solution to produce a classical , top–down drawing of rooted trees. Eades [4] also described an alternative, so called radial display of a tree, based on earlier results described, for instance, in [2]. However, the need for suitable tree representations for large amounts of data still simulates work in finding alternative layouts. For example, there has been an increased interest recently in The classical, top–down drawing of trees has the advantage of being well–known and widely used in many applications. Its use for displaying hierarchies benefits from its natural interpretation. In some cases, however, one might need to deal with representations where the hierarchical organization of data is much less relevant. As an example, we encountered situations (e.g., in exploring keyword and thesauri data) where the hierarchy was not natural, although the underlying data structure was indeed a tree. Eades [4] cites some other examples for what he calls " free trees ". Data in all these applications can of course be described through rooted trees, but only artificially; in fact, exploration in these applications consist in " changing " a root. In our case, our users felt that the classical …