to use diagrams to
visualize the results of a complex request inside a graphical interface
for traditional library environments. Such a representation allows the
user to perceive simultaneously the results of his query and the
relevance of the database according to the query.
shown by a constructive method
the existence of a planar diagrammatic representation called extended
Euler diagrams, derived from the Euler diagram representation, for any
collection of sets X1,...,Xn , n <
9. These diagrams are adapted for representing sets inclusions
and intersections: each set Xi and each non empty
intersection of a subcollection of X1,...,Xn
is represented by a unique connected region of the plane.
Moreover, using the notion of planarity and drawing for hypergraphs
introduced respectively by Johnson and Pollak in 1987 and Mäkinen
in 1990, we have shown that any hypergraph having less than nine
hyperedges is vertex-planar and can be drawn in the edge standard and
in the subset standard without edge crossing.
We are currently
implementing a system drawing automatically a planar extended
Euler Diagram from any configuration involving less than nine sets.
Here are somme preliminary results :
Verroust and M-L. Viaud. Ensuring
the drawability of Extended Euler Diagrams for up to 8 sets. In Rapport
INRIA no 4973. October 2003.
Verroust and M-L. Viaud.
the drawability of Extended Euler Diagrams for up to 8 sets. (reduced
version) Diagrams'2004. International Conference on the Theory and
Application of Diagrams, Cambridge, March 2004.[pdf]
Email : Anne.Verroust(@)inria.fr
Adress : INRIA - BP 105,
78153 Le Chesnay Cedex - FRANCE
Phone : (+33 1) 39 63 54 41
Fax : (+33 1) 39 63 59 95
Secretary : (+33 1) 39 63 53 74