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,..., 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.