Integrating Edge Routing into Force-Directed Layout

  • Tim Dwyer
  • Kim Marriott
  • Michael Wybrow
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4372)

Abstract

The typical use of force-directed layout is to create organic-looking, straight-edge drawings of large graphs while combinatorial techniques are generally preferred for high-quality layout of small to medium sized graphs. In this paper we integrate edge-routing techniques into a force-directed layout method based on constrained stress majorisation. Our basic procedure takes an initial layout for the graph, including poly-line paths for the edges, and improves this layout by moving the nodes to reduce stress and moving edge bend points to straighten the edges and reduce their overall length. Separation constraints between nodes and edge bend points are used to ensure that nodes do not overlap edges or other nodes and that no additional edge crossings are introduced.

Keywords

graph layout constrained optimisation force-directed layout edge routing 

References

  1. 1.
    Fisk, C.J., Isett, D.D.: ACCEL: automated circuit card etching layout. In: DAC’65: Proceedings of the SHARE design automation project, pp. 1–9. 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)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bertault, F.: A force-directed algorithm that preserves edge crossing properties. In: Kratochvíl, J. (ed.) GD 1999. LNCS, vol. 1731, pp. 351–358. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  4. 4.
    Brandes, U., Wagner, D.: Using graph layout to visualize train interconnection data. In: Whitesides, S.H. (ed.) GD 1998. LNCS, vol. 1547, pp. 44–56. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  5. 5.
    Finkel, B., Tamassia, R.: Curvilinear graph drawing using the force-directed method. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 448–453. Springer, Heidelberg (2005)Google Scholar
  6. 6.
    Dwyer, T., Koren, Y., Marriott, K.: IPSep-CoLa: An incremental procedure for separation constraint layout of graphs. In: Proc. IEEE Symp. on Information Visualisation (Infovis’06), IEEE Computer Society Press, Los Alamitos (To appear, 2006)Google Scholar
  7. 7.
    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
  8. 8.
    Fruchterman, T., Reingold, E.M.: Graph drawing by force-directed placement. Software - Practice and Experience 21, 1129–1164 (1991)CrossRefGoogle Scholar
  9. 9.
    Gutwenger, C., Mutzel, P., Weiskircher, R.: Inserting an edge into a planar graph. In: SODA ’01: Proc. of the 12th Annual ACM-SIAM Symp. on Discrete Algorithms, pp. 246–255. ACM Press, New York (2001)Google Scholar
  10. 10.
    Garey, M.R., Johnson, D.S.: Crossing number is NP-complete. Journal of Algebraic Discrete Methods 4(3), 312–316 (1983)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Harel, D., Sardas, M.: Randomized graph drawing with heavy-duty preprocessing. In: AVI ’94: Proceedings of the Workshop on Advanced Visual Interfaces, Bari, Italy, pp. 19–33. ACM Press, New York (1994), doi:10.1145/192309.192319CrossRefGoogle Scholar
  12. 12.
    Wybrow, M., Marriott, K., Stuckey, P.J.: Incremental connector routing. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 446–457. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Purchase, H.C., Cohen, R.F., James, M.: Validating graph drawing aesthetics. In: North, S.C. (ed.) GD 1996. LNCS, vol. 1190, pp. 435–446. Springer, Heidelberg (1997)Google Scholar
  14. 14.
    Ware, C., Purchase, H., Colpoys, L., McGill, M.: Cognitive measurements of graph aesthetics. Information Visualization 1(2), 103–110 (2002)CrossRefGoogle Scholar
  15. 15.
    Dobkin, D.P., Gansner, E.R., Koutsofios, E., North, S.C.: Implementing a general-purpose edge router. In: DiBattista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 262–271. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  16. 16.
    Freivalds, K.: Curved edge routing. In: Freivalds, R. (ed.) FCT 2001. LNCS, vol. 2138, pp. 126–137. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  17. 17.
    Preparata, F.P., Shamos, M.I.: Computational Geometry, pp. 359–365. Springer, Heidelberg (1985)Google Scholar
  18. 18.
    Dwyer, T., Marriott, K., Stuckey, P.: Fast node overlap removal. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 153–164. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Tim Dwyer
    • 1
  • Kim Marriott
    • 1
  • Michael Wybrow
    • 1
  1. 1.Clayton School of Information Technology, Monash University, Clayton, Victoria 3800Australia

Personalised recommendations