An Experimental Study on Distance-Based Graph Drawing

(Extended Abstract)
  • Ulrik Brandes
  • Christian Pich
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5417)

Abstract

In numerous application areas, general undirected graphs need to be drawn, and force-directed layout appears to be the most frequent choice. We present an extensive experimental study showing that, if the goal is to represent the distances in a graph well, a combination of two simple algorithms based on variants of multidimensional scaling is to be preferred because of their efficiency, reliability, and even simplicity. We also hope that details in the design of our study help advance experimental methodology in algorithm engineering and graph drawing, independent of the case at hand.

References

  1. 1.
    Borg, I., Groenen, P.J.F.: Modern Multidimensional Scaling, 2nd edn. Springer, Heidelberg (2005)MATHGoogle Scholar
  2. 2.
    Brandenburg, F.-J., Himsolt, M., Rohrer, C.: An experimental comparison of force-directed and randomized graph drawing algorithms. In: Brandenburg, F.J. (ed.) GD 1995. LNCS, vol. 1027, pp. 76–87. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  3. 3.
    Brandes, U.: Drawing on physical analogies. In: Kaufmann, M., Wagner, D. (eds.) Drawing Graphs. LNCS, vol. 2025, pp. 71–86. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Brandes, U., Pich, C.: Eigensolver methods for progressive multidimensional scaling of large data. In: Kaufmann, M., Wagner, D. (eds.) GD 2006. LNCS, vol. 4372, pp. 42–53. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Buja, A., Swayne, D.F.: Visualization methodology for multidimensional scaling. Journal of Classification 19, 7–43 (2002)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Civril, A., Magdon-Ismail, M., Bocek-Rivele, E.: SSDE: Fast graph drawing using sampled spectral distance embedding. In: Kaufmann, M., Wagner, D. (eds.) GD 2006. LNCS, vol. 4372, pp. 30–41. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Cohen, J.D.: Drawing graphs to convey proximity. ACM Transactions on Computer-Human Interaction 4(3), 197–229 (1997)CrossRefGoogle Scholar
  8. 8.
    Cox, T.F., Cox, M.A.A.: Multidimensional Scaling, 2nd edn. CRC/Chapman and Hall, Boca Raton (2001)MATHGoogle Scholar
  9. 9.
    Eades, P., Wormald, N.C.: Fixed edge-length graph drawing is NP-hard. Discrete Applied Mathematics 28(2), 111–134 (1990)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Freeman, L.C.: Graph layout techniques and multidimensional analysis. Journal of Social Structure 1 (2000)Google Scholar
  11. 11.
    Gajer, P., Kobourov, S.: GRIP – Graph drawing with intelligent placement. In: Marks, J. (ed.) GD 2000. LNCS, vol. 1984, pp. 222–228. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Gansner, E.R., Koren, Y., North, S.C.: Graph drawing by stress majorization. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 239–250. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  13. 13.
    Hachul, S., Jünger, M.: An experimental comparison of fast algorithms for drawing general large graphs. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 235–250. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Harel, D., Koren, Y.: Graph drawing by high-dimensional embedding. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 207–219. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Kamada, T., Kawai, S.: An algorithm for drawing general undirected graphs. Information Processing Letters 31, 7–15 (1989)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Kruskal, J.B., Seery, J.B.: Designing network diagrams. In: Proc. First General Conference on Social Graphics, pp. 22–50 (1980)Google Scholar
  17. 17.
    Kruskal, J.B.: Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 29(1), 1–27 (1964)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    de Leeuw, J.: Applications of convex analysis to multidimensional scaling. In: Barra, J.R., Brodeau, F., Romier, G., van Cutsem, B. (eds.) Recent Developments in Statistics, pp. 133–145. North-Holland, Amsterdam (1977)Google Scholar
  19. 19.
    McGee, V.E.: The multidimensional scaling of “elastic” distances. Br. J. Math. Stat. Psychol. 19, 181–196 (1966)CrossRefGoogle Scholar
  20. 20.
    Sammon, J.W.: A nonlinear mapping for data structure analysis. IEEE Transactions on Computers 18(5), 401–409 (1969)CrossRefGoogle Scholar
  21. 21.
    Sibson, R.: Studies in the robustness of multidimensional scaling: Procrustes statistics. J. R. Stat. Sooc. 40(2), 234–238 (1978)MATHMathSciNetGoogle Scholar
  22. 22.
    de Silva, V., Tenenbaum, J.B.: Sparse multidimensional scaling using landmark points. Tech. rep., Stanford University (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Ulrik Brandes
    • 1
  • Christian Pich
    • 1
  1. 1.Department of Computer & Information ScienceUniversity of KonstanzGermany

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