DocumentCode :
1907980
Title :
Efficiently drawing a significant spanning tree of a directed graph
Author :
Harrigan, Martin ; Healy, Patrick
Author_Institution :
Dept. of Comput. Sci. & Inf. Syst., Limerick Univ.
fYear :
2007
fDate :
5-7 Feb. 2007
Firstpage :
53
Lastpage :
59
Abstract :
A directed graph can model any ordered relationship between objects. However, visualizing such graphs can be a challenging task. If the graph is undirected, a popular strategy is to choose a significant spanning tree, nominate a vertex as the root, for example the vertex whose distance from all other vertices is minimal, hang the significant spanning subtrees from this root and add in the remaining edges in some unobtrusive manner. In the directed case the spanning tree is a tree DAG (a directed graph without any undirected cycles) and not simply a directed tree with one appropriate root. It may have multiple sources (vertices with indegree equal to zero) that all warrant root status and so the undirected approach must be modified somewhat. In this paper, we present a method of drawing directed graphs that emphasizes a significant spanning tree. It can be considered a variation of the Sugiyama framework in that it combines two steps of the framework (leveling and crossing minimisation) by finding, in linear time, a leveling of the graph that is level planar with respect to some spanning tree and restricting the permutations of the vertices on each level to those that constitute a level planar embedding of this subgraph. The edges of the spanning tree will therefore not cross each other. Using the globally oriented Fiedler vector we choose permutations of the vertices on each level that reduce the number of crossings between the remaining edges.
Keywords :
computational geometry; data visualisation; directed graphs; minimisation; trees (mathematics); vectors; crossing minimisation; directed graph visualization; globally oriented Fiedler vector; spanning tree drawing; Computer languages; Computer science; Information systems; Minimization methods; Packaging; Tree graphs; Vectors; Visualization;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Visualization, 2007. APVIS '07. 2007 6th International Asia-Pacific Symposium on
Conference_Location :
Sydney, NSW
Print_ISBN :
1-4244-0808-3
Electronic_ISBN :
1-4244-0809-1
Type :
conf
DOI :
10.1109/APVIS.2007.329275
Filename :
4126218
Link To Document :
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