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

Abstract : 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.
Keywords : Euler diagrams
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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⟩

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