DAG Drawing from an Information Visualization Perspective

Abstract

When dealing with a graph, any visualization strategy must rely on a layout procedure at least to initiate the process. Because the visualization process evolves within an interactive environment the choice of this layout procedure is critical and will often be based on efficiency.This paper compares two popular layout strategies, one based on the extraction of a spanning tree, the other based on edge crossing minimization of directed acyclic graphs. The comparison is made based on a large number of experimental evidence gathered through random graph generation. The main conclusion of these experiments is that, contrary to the popular belief, usage of edge crossing minimization algorithms may be extremely useful and advantageous, even under the heavy requirements of information visualization.

Exploring Multiple Trees through DAG Representations

“…Trees that construct their own structure over shared nodes are more problematic as the differing tree structures produce significant extra edge-crossings in the agglomeration style views. Techniques specifically developed for drawing DAGs can however impose a global orientation for parent-child links on the structure if the trees all have the same parent-child orientation -that is a node closer to the root than another node in one tree will always maintain that characteristic in another tree -though the restrictions on node placement involves a trade-off on edge crossings as seen in Melançon et al [29]. Linnean taxonomic classifications have this property, through being organised using an immutable set of ordered ranks, though other hierarchical structures such as phylogenies are not guaranteed to have this property, and Robertson et al's [30] polyarchy structures in effect may construct trees freely from a pool of nodes regardless of those nodes' positioning in other trees.…”

“…Minor averages are calculated using the node positions in the previous layer, and are used to tiebreak if the major average values are the same for any nodes. Melançon et al [29] used the concept of calculating averages for nodes in a layer from all their neighbouring node positions after performing the original upwards or downwards-only calculation to reduce the number of iterations needed to stabilise a DAG layout, but did not differentiate between the two types. This method can stop some simple superfluous edge crossings at the cost of some extra calculations.…”

Depth-First Discovery Algorithm for incremental topological sorting of directed acyclic graphs

“…We compared the performance of DA and DFDA on random DAGs generated by DagAlea [4]. For uniformity, algorithms were implemented using LEDA [3], with Fibonacci heap priority queues.…”

A Survey of Multiple Tree Visualisation

“…A general graph layout method also usually results in no global orientation for child-parent links even if one exists in the overall structure. Techniques specifically developed for drawing DAGs can re-impose a global orientation for parent-child links, though the restrictions on node placement involves a trade-off on edge crossings as seen in Graham & Kennedy 57 , D'Ambros et al 110 and Melançon & Herman 111 . The main advantage with agglomeration displays is that screen space is effectively re-used across tree representations.…”