Abstract
The Sugiyama framework is the most commonly used concept for visualizing directed graphs. It draws them in a hierarchical way and operates in four phases: cycle removal, leveling, crossing reduction, and coordinate assignment. However, there are situations where cycles must be displayed as such, e. g., distinguished cycles in the biosciences and scheduling processes which repeat in a daily or weekly turn. This excludes the removal of cycles. In their seminal paper Sugiyama et al. introduced recurrent hierarchies as a concept to draw graphs with cycles. However, this concept has not received much attention in the following years. In this paper we supplement our cyclic Sugiyama framework and investigate the coordinate assignment phase. We provide an algorithm which runs in linear time and constructs drawings which have at most two bends per edge and use quadratic area.
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References
Bachmaier, C., Brandenburg, F.J., Brunner, W., Lovász, G.: Cyclic leveling of directed graphs. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 348–359. Springer, Heidelberg (2009)
Bachmaier, C., Brandenburg, F.J., Forster, M., Holleis, P., Raitner, M.: Gravisto: Graph visualization toolkit. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 502–503. Springer, Heidelberg (2005), http://gravisto.fim.uni-passau.de/
Brandes, U., Köpf, B.: Fast and simple horizontal coordinate assignment. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) GD 2001. LNCS, vol. 2265, pp. 31–44. Springer, Heidelberg (2002)
Garey, M.R., Johnson, D.S.: A Guide to the Theory of NP-Completeness. W.H. Freemann, New York (1979)
Hübner, F.: A Global Approach on Crossing Minimization in Hierarchical and Cyclic Layouts of Leveled Graphs. Master’s thesis, University of Passau (2009)
Kaufmann, M., Wagner, D. (eds.): Drawing Graphs. LNCS, vol. 2025. Springer, Heidelberg (2001)
Michal, G. (ed.): Biochemical Pathways: An Atlas of Biochemistry and Molecular Biology. Wiley, Chichester (1998)
Serafini, P., Ukovich, W.: A mathematical model for periodic scheduling problems. SIAM J. Discrete Math. 2(4), 550–581 (1989)
Sugiyama, K., Tagawa, S., Toda, M.: Methods for visual understanding of hierarchical system structures. IEEE Trans. Syst., Man, Cybern. 11(2), 109–125 (1981)
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Bachmaier, C., Brandenburg, F.J., Brunner, W., Fülöp, R. (2009). Coordinate Assignment for Cyclic Level Graphs. In: Ngo, H.Q. (eds) Computing and Combinatorics. COCOON 2009. Lecture Notes in Computer Science, vol 5609. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02882-3_8
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DOI: https://doi.org/10.1007/978-3-642-02882-3_8
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