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.

On the validity of hierarchical decompositions / Finocchi, Irene; Petreschi, Rossella. - STAMPA. - 2108:(2001), pp. 368-374. (Intervento presentato al convegno 7th Annual International Conference on Computing and Combinatorics tenutosi a GUILIN, PEOPLES R CHINA nel AUG 20-23, 2001) [10.1007/3-540-44679-6_40].

On the validity of hierarchical decompositions

FINOCCHI, Irene;PETRESCHI, Rossella
2001

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.
2001
9783540424949
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/251907
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