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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
