Abstract Euler Diagram Isomorphism

Euler diagrams are widely used for information visualization and form the basis of a variety of formal languages that are used to express constraints in computing. Tools to automatically generate and layout these diagrams from an abstract description have to overcome the fact that this problem is computationally difficult. We develop a theory of isomorphism of diagram descriptions and identify invariants of these descriptions under isomorphism. We can apply this theory to improve the efficiency of the generation of all abstract descriptions (up to isomorphism). We can also consider the production and use of libraries of diagrams with nice visual properties: by providing a normal form for the abstract descriptions we can improve efficiency of searches for isomorphic diagrams within such libraries and, moreover, utilize invariants for further efficiency savings. We produce an implementation of the theory and give an indication of the efficiency improvements.