Abstract Euler diagram isomorphism

Gem Stapleton, Andrew Fish, Peter Rodgers

Research output: Chapter in Book/Conference proceeding with ISSN or ISBNConference contribution with ISSN or ISBN

Abstract

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.
Original languageEnglish
Title of host publicationProceedings of the 14th International Conference on Distributed Multimedia Systems
Place of PublicationSkokie, IL, USA
PublisherKnowledge Systems Institute
Pages310-317
Number of pages8
Publication statusPublished - 1 Sep 2008
EventProceedings of the 14th International Conference on Distributed Multimedia Systems - Boston, Massachusetts, USA, 4-6 September, 2008
Duration: 1 Sep 2008 → …

Conference

ConferenceProceedings of the 14th International Conference on Distributed Multimedia Systems
Period1/09/08 → …

Keywords

  • Euler Diagrams
  • Venn Diagrams
  • Hypergraph Isomorphism

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    Stapleton, G., Fish, A., & Rodgers, P. (2008). Abstract Euler diagram isomorphism. In Proceedings of the 14th International Conference on Distributed Multimedia Systems (pp. 310-317). Knowledge Systems Institute. http://www.cem.brighton.ac.uk/users/ges9/VLC2008a.pdf