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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 X_1,...,X_n , n<9. These diagrams are adapted for representing sets inclusions and intersections: each set X_i and each non empty intersection of a subcollection of X_1,...,X_n is represented by a unique connected region of the plane. Starting with a 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 X_1,...,X_n. These diagrams will be used to visualize the results of a complex request on any indexed video database. 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. Venn, hypergraphes, planarité de graphe, visualisation de données
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Submitted on : Tuesday, May 23, 2006 - 6:13:52 PM
Last modification on : Thursday, February 3, 2022 - 11:18:43 AM
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  • HAL Id : inria-00071605, version 1



Anne Verroust, Marie-Luce Viaud. Ensuring the Drawability of Extended Euler Diagrams for up to 8 Sets. [Research Report] RR-4973, INRIA. 2003. ⟨inria-00071605⟩



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