Abstract
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.
Work partially supported by the project “Algorithms for Large Data Sets: Science and Engineering” of the Italian Ministry of University and of Scientific and Technological Research (MURST 40%).
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Finocchi, I., Petreschi, R. (2001). On the Validity of Hierarchical Decompositions. In: Wang, J. (eds) Computing and Combinatorics. COCOON 2001. Lecture Notes in Computer Science, vol 2108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44679-6_40
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DOI: https://doi.org/10.1007/3-540-44679-6_40
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