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A graph theoretic approach to general euler diagram drawing

By Gem Stapleton, John Howse and Peter Rodgers

Abstract

Euler diagrams are used in a wide variety of areas for representing information about relationships between collections of objects. Recently, several techniques for automated Euler diagram drawing have been proposed, contributing to the Euler diagram generation problem: given an abstract description, draw an Euler diagram with that description and which possesses certain properties, sometimes called well-formedness conditions. We present the first fully formalized, general framework that permits the embedding of Euler diagrams that possess any collection of the six typically considered well-formedness conditions. Our method first converts the abstract description into a vertex-labelled graph. An Euler diagram can then be formed, essentially by finding a dual graph of such a graph. However, we cannot use an arbitrary plane embedding of the vertex-labelled graph for this purpose. We identify specific embeddings that allow the construction of appropriate duals. From these embeddings, we can also identify precisely which properties the drawn Euler diagram will possess and 'measure' the number of times that each well-formedness condition is broken. We prove that every abstract description can be embedded using our method. Moreover, we identify exactly which (large) class of Euler diagrams can be generated

Topics: G000 Computing and Mathematical Sciences
Publisher: Elsevier
Year: 2010
DOI identifier: 10.1016/j.tcs.2009.09.005
OAI identifier: oai:eprints.brighton.ac.uk:8162

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Citations

  1. (2005). A system for virtual directories using Euler diagrams, in: doi
  2. (2007). Automated theorem proving in Euler diagrams systems, doi
  3. Chronic kidney disease care delivered by us family medicine and internal medicine trainees: results from an online survey,
  4. (2005). Collaborative knowledge capture in ontologies, in: doi
  5. (2006). Defining health/illness: Societal and/or clinical medicine?,
  6. (2003). Drawing area-proportional Venn and Euler diagrams, in: doi
  7. (2004). Ensuring the drawability of Euler diagrams for up to eight sets, in: doi
  8. (2004). Failure mode modular de-composition using spider diagrams, in: doi
  9. (2008). General Euler diagram generation, in: doi
  10. (2005). Generalized Venn diagrams: A new method for visualizing complex genetic set relations, doi
  11. (2007). Generating and drawing area-proportional Euler and Venn diagrams, doi
  12. (2008). Generating Euler diagrams from existing layouts, in: Layout of (Software) Engineering Diagrams,
  13. (2002). Generating Euler diagrams, in: doi
  14. (1775). Lettres a une princesse dallemagne sur divers sujets de physique et de philosophie, doi
  15. (1995). Logic and Visual Information, doi
  16. (2005). Longitudinal changes in the visual field and optic disc in glaucoma, doi
  17. On the diagrammatic and mechanical representation of propositions and reasonings, doi
  18. (2007). Properties of Euler diagrams, in: doi
  19. (1997). Spatial logic and the complexity of diagrammatic reasoning,
  20. (2005). Towards a general solution to drawing area-proportional Euler diagrams, in: doi
  21. (2002). Towards a visual editing environment for the languages of the semantic web,
  22. (2004). Using DAG transformations to verify Euler/Venn homogeneous and Euler/Venn FOL heterogeneous rules of inference, doi
  23. (2004). Using Euler diagrams in traditional library environments, in: doi
  24. (1989). Venn diagrams for many sets., doi
  25. (2003). VennFS: A Venn diagram file manager, in: doi
  26. Vennmaster: Area-proportional Euler diagrams for functional go analysis of microarrays, doi
  27. (2008). Visualise undrawable Euler diagrams, in: doi
  28. (1999). Visualization of formal specifications, in: doi

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