Abstract
We describe a method for drawing graph-enhanced Euler diagrams using a three stage method. The first stage is to lay out the underlying Euler diagram using a multicriteria optimizing system. The second stage is to find suitable locations for nodes in the zones of the Euler diagram using a force based method. The third stage is to minimize edge crossings and total edge length by swapping the location of nodes that are in the same zone with a multicriteria hill climbing method. We show a working version of the software that draws spider diagrams. Spider diagrams represent logical expressions by superimposing graphs upon an Euler diagram. This application requires an extra step in the drawing process because the embedded graphs only convey information about the connectedness of nodes and so a spanning tree must be chosen for each maximally connected component. Similar notations to Euler diagrams enhanced with graphs are common in many applications and our method is generalizable to drawing Hypergraphs represented in the subset standard, or to drawing Higraphs where edges are restricted to connecting with only atomic nodes.
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References
Bertault, F., Eades, P.: Drawing Hypergraphs in the Subset Standard. In: Marks, J. (ed.) GD 2000. LNCS, vol. 1984, pp. 164–169. Springer, Heidelberg (2001)
De Chiara, R., Erra, U., Scarano, V.: VENNFS: A Venn-Diagram File Manager. In: IEEE Proceedingsof Information Visualization (IV 2003), pp. 120–126 (2003)
Consens, M.P., Mendelzon, A.O.: Hy+: A Hygraph-based Query and Visualization System. In: Proc. of the ACM SIGMOD Int. Conf. on Management of Data, pp. 511–516 (1993)
Eades, P., Feng, Q.: Multilevel Visualization of Clustered Graphs. In: North, S.C. (ed.) GD 1996. LNCS, vol. 1190, pp. 101–112. Springer, Heidelberg (1997)
Fish, A., Flower, J., Howse, J.: A Reading Algorithm for Constraint Diagrams. In: Proc. IEEE 2003 symposium on Human-Centric Computing languages and environments (HCC 2003), pp. 161–168 (2003)
Fish, A., Howse, J.: Computing Reading Trees for Constraint Diagrams. In: Pfaltz, J.L., Nagl, M., Böhlen, B. (eds.) AGTIVE 2003. LNCS, vol. 3062, pp. 260–274. Springer, Heidelberg (2004)
Flower, J., Howse, J.: Generating Euler Diagrams. In: Hegarty, M., Meyer, B., Narayanan, N.H. (eds.) Diagrams 2002. LNCS (LNAI), vol. 2317, pp. 61–75. Springer, Heidelberg (2002)
Flower, J., Rodgers, P., Mutton, P.: Layout Metrics for Euler Diagrams. In: Proc. IEEE Information Visualization (IV 2003), pp. 272–280 (2003)
Flower, J., Stapleton, G.: Automated Theorem Proving with Spider Diagrams. To appear in Proc. Computing Australasian Theory Symposium (CATS 2004)
Flower, J., Masthoff, J., Stapleton, G.: Generating Readable Proofs: A Heuristic Approach to Theorem Proving With Spider Diagrams. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds.) Diagrams 2004. LNCS (LNAI), vol. 2980, Springer, Heidelberg (2004)
Flower, J., Howse, J., Taylor, J.: Nesting in Euler Diagrams, Syntax, Semantics and Construction. Journal of Software and Systems Modelling (SoSyM), Springer Verlag, Issue 1, article 5
Fruchterman, T.M.J., Reingold, E.M.: Graph Drawing by Force-directed Placement. Software-Practice and Experience 21(11), 1129–1164 (1991)
Harel, D.: On Visual Formalisms. Communications of the ACM 31(5), 514–530 (1988)
Harel, D., Yashchin, G.: An Algorithm for Blob Hierarchy Layout. In: Working Conference on Advanced Visual Interfaces, May 2000, pp. 29–40 (2000)
Higraph web page, http://db.uwaterloo.ca/~gweddell/higraph/higraph.html
Howse, J., Molina, F., Taylor, J., Kent, S.: Reasoning with Spider Diagrams. In: Proc. IEEE Symposium on Visual Languages 1999 (VL 1999), pp. 138–147. IEEE Press, Los Alamitos (1999)
Mäkinen, E.: How to draw a hypergraph. International Journal of Computer Mathematics 34, 177–185 (1990)
Stapleton, G., Howse, J., Taylor, J., Thompson, S.: What Can Spider Diagrams Say? In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds.) Diagrams 2004. LNCS (LNAI), vol. 2980, Springer, Heidelberg (2004)
Stapleton, G., Howse, J., Taylor, J.: A Constraint Diagram Reasoning System. In: Proc Visual Languages and Computing 2003, pp. 263–270 (2003)
Visual Modelling Group: technical report on spider diagram reasoning systems at www.cmis.brighton.ac.uk/research/vmg/SDRules.html
Davidson, R., Harel, D.: Drawing Graphs Nicely Using Simulated Annealing. ACM Transactions of Graphics 15(4), 301–331 (1996)
Chow, S., Ruskey, F.: Drawing Area-Proportional Venn and Euler Diagrams. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 466–477. Springer, Heidelberg (2004)
Howse, J., Molina, F., Taylor, J.: On the completeness and expressiveness of spider diagram systems. In: Anderson, M., Cheng, P., Haarslev, V. (eds.) Diagrams 2000. LNCS (LNAI), vol. 1889, pp. 26–41. Springer, Heidelberg (2000)
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Mutton, P., Rodgers, P., Flower, J. (2004). Drawing Graphs in Euler Diagrams. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds) Diagrammatic Representation and Inference. Diagrams 2004. Lecture Notes in Computer Science(), vol 2980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25931-2_9
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DOI: https://doi.org/10.1007/978-3-540-25931-2_9
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