Ensuring the Drawability of Extended Euler Diagrams for up to 8 Sets

Anne Verroust (1) , Marie-Luce Viaud (2)

1 IMEDIA - Image and multimedia indexing, browsing and retrieval
2 INA - Institut National de l'Audiovisuel

This paper shows by a constructive method the existence of a diagrammatic representation called extended Euler diagrams 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. Starting with an abstract description of the diagram, we define the dual graph G and reason with the properties of this graph to build a planar representation of the X1, ..., Xn. These diagrams will be used to visualize the results of a complex request on any indexed video databases. In fact, such a representation allows the user to perceive simultaneously the results of his query and the relevance of the database according to the query.

Mots clés: Euler diagrams

Domaines: Informatique [cs]; Algorithme et structure de données [cs.DS]

Anne Verroust, Marie-Luce Viaud. Ensuring the Drawability of Extended Euler Diagrams for up to 8 Sets. Diagrammatic Representation and Inference, Diagrams 2004, Mar 2004, Cambridge, United Kingdom. ⟨10.1007/978-3-540-25931-2_13⟩. ⟨hal-01225189⟩