Smoother Transitions Between Breadth-First-Spanning-Tree-Based Drawings

We demonstrate a collection of techniques that seek to make the transition between drawings based on two topologically distinct spanning trees of the same graph as clear as possible. As Herman, Melançon, and Marshall note [HMM00], one way to draw a large graph is to extract a spanning tree from it, use a tree layout algorithm [CK95, Ead92, RT81, II90, TM02, GADM04, LY05] to draw the spanning tree, and then add back the graph edges not included in the spanning tree. The problem with this approach is that the drawings tend to favor the edges that are part of the spanning tree, even though they may be no more important in the underlying structure than non-spanning tree edges. One way of dealing with this problem is to facilitate exploration of multiple spanning trees. Yee et al. [YFDH01] describe a system that produces layouts based on Eades’ radial layout algorithm [Ead92] and lets users interactively select a new node as root. When this happens, the system first calculates a breadth-first spanning tree rooted at the selected node, and then smoothly transitions to a topologically distinct spanning tree. Although Yee et al.’s static layouts are free of edge crossings, transitions between trees can be hard to follow because there edge crossings do occur. A number of tree-based graph visualizations, such as RINGS [TM02], RDT [JP98], and others [LRP95, Mun97, Wil99] also allow users to reconfigure views of a given tree, and some even allow users to change the root node. They do not, however, let the user select and smoothly transition to a different spanning tree built from a different collection of edges. To our knowledge only Yee et al.’s system [YFDH01] and one mentioned by Melançon and Herman [MH98] support smooth transitions between different spanning trees of the same graph. We have built a system to use as a test bed for improving the sort of transitions between topologically distinct graphs that Yee et al. and Melançon and Herman use. Here we present some preliminary results. Like Yee et al. we only use breadth-first search trees. These often share common subtrees, especially when the roots of the trees are closely related. A major thrust of our research concerns layouts that make it easier for users to perceive the migration of these common subtrees as they disconnect from their old parents, and then reconnect at their new parents’ locations. As illustrated in our poster, our static layouts, use a variant of what Lin and Yen call “a balloon drawing subtree with non-uniform size” [LY05] (flattenedout cone drawings [CK95, JP98]) rather than the radial layout of Eades [Ead92]