Edge Routing with Ordered Bundles

  • Sergey Pupyrev
  • Lev Nachmanson
  • Sergey Bereg
  • Alexander E. Holroyd
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7034)


We propose a new approach to edge bundling. At the first stage we route the edge paths so as to minimize a weighted sum of the total length of the paths together with their ink. As this problem is NP-hard, we provide an efficient heuristic that finds an approximate solution. The second stage then separates edges belonging to the same bundle. To achieve this, we provide a new and efficient algorithm that solves a variant of the metro-line crossing minimization problem. The method creates aesthetically pleasing edge routes that give an overview of the global graph structure, while still drawing each edge separately, without intersecting graph nodes, and with few crossings.


Edge Route Dijkstra Algorithm Edge Segment Clockwise Order Edge Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Chen, H.-F.S., Lee, D.T.: On crossing minimization problem. IEEE Transactions on Computer-aided Design of Integrated Circuits and Systems 17, 406–418 (1998)CrossRefGoogle Scholar
  2. 2.
    Cui, W., Zhou, H., Qu, H., Wong, P.C., Li, X.: Geometry-based edge clustering for graph visualization. IEEE Trans. on Visualization and Computer Graphics 14(6), 1277–1284 (2008)CrossRefGoogle Scholar
  3. 3.
    Dwyer, T., Nachmanson, L.: Fast Edge-Routing for Large Graphs. In: Eppstein, D., Gansner, E.R. (eds.) GD 2009. LNCS, vol. 5849, pp. 147–158. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Gansner, E., Hu, Y., North, S., Scheidegger, C.: Multilevel agglomerative edge bundling for visualizing large graphs. In: Proc. IEEE Pacific Visualization Symposium (to appear, 2011)Google Scholar
  5. 5.
    Gansner, E.R., Koren, Y.: Improved Circular Layouts. In: Kaufmann, M., Wagner, D. (eds.) GD 2006. LNCS, vol. 4372, pp. 386–398. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York (1979)zbMATHGoogle Scholar
  7. 7.
    Guttman, A.: R-trees: A dynamic index structure for spatial searching. In: Proc. Int. Conf. on Management of Data, pp. 47–57 (1984)Google Scholar
  8. 8.
    Holten, D.: Hierarchical edge bundles: Visualization of adjacency relations in hierarchical data. IEEE Transactions on Visualization and Computer Graphics 12(5), 741–748 (2006)CrossRefGoogle Scholar
  9. 9.
    Holten, D., van Wijk, J.J.: Force-directed edge bundling for graph visualization. Computer Graphics Forum 28(3), 983–990 (2009)CrossRefGoogle Scholar
  10. 10.
    Lambert, A., Bourqui, R., Auber, D.: Winding Roads: Routing edges into bundles. Computer Graphics Forum 29(3 ), 853–862 (2010)CrossRefGoogle Scholar
  11. 11.
    Nachmanson, L., Robertson, G., Lee, B.: Drawing Graphs with GLEE. In: Hong, S.-H., Nishizeki, T., Quan, W. (eds.) GD 2007. LNCS, vol. 4875, pp. 389–394. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Nöllenburg, M.: An Improved Algorithm for the Metro-Line Crossing Minimization Problem. In: Eppstein, D., Gansner, E.R. (eds.) GD 2009. LNCS, vol. 5849, pp. 381–392. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Pupyrev, S., Nachmanson, L., Kaufmann, M.: Improving Layered Graph Layouts with Edge Bundling. In: Brandes, U., Cornelsen, S. (eds.) GD 2010. LNCS, vol. 6502, pp. 329–340. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sergey Pupyrev
    • 1
  • Lev Nachmanson
    • 2
  • Sergey Bereg
    • 3
  • Alexander E. Holroyd
    • 2
  1. 1.Ural State UniversityRussia
  2. 2.Microsoft ResearchUSA
  3. 3.University of Texas at DallasUSA

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