Drawing Graphs within Restricted Area

  • Maximilian Aulbach
  • Martin Fink
  • Julian Schuhmann
  • Alexander Wolff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8871)

Abstract

We study the problem of selecting a maximum-weight subgraph of a given graph such that the subgraph can be drawn within a prescribed drawing area subject to given non-uniform vertex sizes. We develop and analyze heuristics both for the general (undirected) case and for the use case of (directed) calculation graphs which are used to analyze the typical mistakes that high school students make when transforming mathematical expressions in the process of calculating, for example, sums of fractions.

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References

  1. 1.
    Java Universal Network/Graph Framework (JUNG), http://www.jung.sourceforge.net
  2. 2.
    Aulbach, M., Fink, M., Schuhmann, J., Wolff, A.: Drawing graphs within restricted area. CoRR (2014), ArXiv e-print http://arxiv.org/abs/1409.0499
  3. 3.
    Bertault, F.: A force-directed algorithm that preserves edge crossing properties. Inf. Proc. Letters 74(1-2), 7–13 (2000)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Coffman, E.G., Graham, R.L.: Optimal scheduling for two-processor systems. Acta Inform. 1(3), 200–213 (1972)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Da Lozzo, G., Di Battista, G., Ingrassia, F.: Drawing graphs on a smartphone. J. Graph Algorithms Appl. 16(1), 109–126 (2012)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Duncan, C.A., Gutwenger, C., Nachmanson, L., Sander, G.: Graph drawing contest report. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 575–579. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  7. 7.
    Dwyer, T., Marriott, K., Schreiber, F., Stuckey, P., Woodward, M., Wybrow, M.: Exploration of networks using overview+detail with constraint-based cooperative layout. IEEE Trans. Vis. Comput. Graph. 14(6), 1293–1300 (2008)CrossRefGoogle Scholar
  8. 8.
    Dwyer, T., Koren, Y., Marriott, K.: IPSep-CoLa: An incremental procedure for separation constraint layout of graphs. IEEE Trans. Vis. Comput. Graph. 12(5), 821–828 (2006)CrossRefGoogle Scholar
  9. 9.
    Dwyer, T., Marriott, K., Wybrow, M.: Topology preserving constrained graph layout. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 230–241. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Fruchterman, T.M.J., Reingold, E.M.: Graph drawing by force-directed placement. Softw. Pract. Exper. 21(11), 1129–1164 (1991)CrossRefGoogle Scholar
  11. 11.
    Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell Syst. Tech. J. 45(9), 1563–1581 (1966)CrossRefGoogle Scholar
  12. 12.
    He, W., Marriott, K.: Constrained graph layout. Constraints 3(4), 289–314 (1998)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Hennecke, M.: Rechengraphen. Math. Didact. 30(1), 68–96 (2007)Google Scholar
  14. 14.
    Patrignani, M.: On the complexity of orthogonal compaction. Comput. Geom. Theory Appl. 19(1), 47–67 (2001)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Sander, G.: A fast heuristic for hierarchical Manhattan layout. In: Brandenburg, F.J. (ed.) GD 1995. LNCS, vol. 1027, pp. 447–458. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  16. 16.
    Simonetto, P., Archambault, D., Auber, D., Bourqui, R.: ImPrEd: An improved force-directed algorithm that prevents nodes from crossing edges. Comput. Graphics Forum 30(3), 1071–1080 (2011)CrossRefGoogle Scholar
  17. 17.
    Sugiyama, K., Tagawa, S., Toda, M.: Methods for visual understanding of hierarchical system structures. IEEE Trans. Syst. Man Cyber. 11(2), 109–125 (1981)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Maximilian Aulbach
    • 1
  • Martin Fink
    • 2
  • Julian Schuhmann
    • 1
  • Alexander Wolff
    • 1
  1. 1.Lehrstuhl für Informatik IUniversität WürzburgGermany
  2. 2.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA

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