Constrained Stress Majorization Using Diagonally Scaled Gradient Projection

  • Tim Dwyer
  • Kim Marriott
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4875)


Constrained stress majorization is a promising new technique for integrating application specific layout constraints into force-directed graph layout. We significantly improve the speed and convergence properties of the constrained stress-majorization technique for graph layout by employing a diagonal scaling of the stress function. Diagonal scaling requires the active-set quadratic programming solver used in the projection step to be extended to handle separation constraints with scaled variables, i.e. of the form s i y i  + g ij  ≤ s j y j . The changes, although relatively small, are quite subtle and explained in detail.


constraints graph layout 


  1. 1.
    Fisk, C.J., Isett, D.D.: ACCEL: automated circuit card etching layout. In: DAC 1965. Proceedings of the SHARE design automation project, pp. 9.1–9.31. ACM Press, New York (1965)Google Scholar
  2. 2.
    Kamada, T., Kawai, S.: An algorithm for drawing general undirected graphs. Information Processing Letters 31, 7–15 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Dwyer, T., Marriott, K., Wybrow, M.: Integrating edge routing into force-directed layout. In: Kaufmann, M., Wagner, D. (eds.) GD 2006. LNCS, vol. 4372, pp. 8–19. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Dwyer, T., Koren, Y., Marriott, K.: IPSep-CoLa: An incremental procedure for separation constraint layout of graphs. IEEE Transactions on Visualization and Computer Graphics 12, 821–828 (2006)CrossRefGoogle Scholar
  5. 5.
    Borg, I., Groenen, P.J.: Modern Multidimensional Scaling: theory and applications, 2nd edn. Springer, Heidelberg (2005)zbMATHGoogle Scholar
  6. 6.
    Gansner, E., Koren, Y., North, S.: Graph drawing by stress majorization. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 239–250. Springer, Heidelberg (2005)Google Scholar
  7. 7.
    Bertsekas, D.P.: Nonlinear Programming. Athena Scientific (1999)Google Scholar
  8. 8.
    Dwyer, T., Marriott, K.: Constrained stress majorization using diagonally scaled gradient projection. Technical Report 217, Clayton School of IT, Monash University (2007)Google Scholar
  9. 9.
    os, P.E., Rényi, A.: On random graphs. Publ. Math. Inst. Hungar. Acad. Sci. 5, 17–61 (1960)Google Scholar
  10. 10.
    Barabási, A.L., Reka, A.: Emergence of scaling in random networks. Science 286, 509–512 (1999)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Tim Dwyer
    • 1
  • Kim Marriott
    • 1
  1. 1.Clayton School of Information TechnologyMonash UniversityClaytonAustralia

Personalised recommendations