Maintaining hierarchical graph views
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Hierarchical Clustering of Trees: Algorithms and Experiments
ALENEX '01 Revised Papers from the Third International Workshop on Algorithm Engineering and Experimentation
Planarity for Clustered Graphs
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Multilevel Visualization of Clustered Graphs
GD '96 Proceedings of the Symposium on Graph Drawing
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Hierarchical decompositions are a useful tool for drawing large graphs. Such decompositions can be represented by means of a data structure called hierarchy tree. In this paper we introduce the notion of P-validity of hierarchy trees with respect to a given property P: this notion reflects the similarity between the topological structure of the original graph and of any high-level representation of it obtained from the hierarchy tree. We study the P-validity when the clustered graph is a tree and property P is the acyclicity, presenting a structure theorem for the P-validity of hierarchy trees under these hypotheses.