Hi-tree Layout Using Quadratic Programming

  • Tim Dwyer
  • Kim Marriott
  • Peter Sbarski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6170)

Abstract

Horizontal placement of nodes in tree layout or layered drawings of directed graphs can be modelled as a convex quadratic program. Thus, quadratic programming provides a declarative framework for specifying such layouts which can then be solved optimally with a standard quadratic programming solver. While slower than specialized algorithms, the quadratic programming approach is fast enough for practical applications and has the great benefit of being flexible yet easy to implement with standard mathematical software. We demonstrate the utility of this approach by using it to layout hi-trees. These are a tree-like structure with compound nodes recently introduced for visualizing the logical structure of arguments and of decisions.

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References

  1. 1.
    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(5), 821–828 (2006)CrossRefGoogle Scholar
  2. 2.
    Dwyer, T., Koren, Y., Marriott, K.: Drawing directed graphs using quadratic programming. IEEE Transactions on Visualization and Computer Graphics 12(4), 536–548 (2006)CrossRefGoogle Scholar
  3. 3.
    He, W., Marriott, K.: Constrained graph layout. Constraints 3, 289–314 (1998)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Bohanec, M.: DEXiTree: A program for pretty drawing of trees. In: Proc. Information Society IS 2007, pp. 8–11 (2007)Google Scholar
  5. 5.
    Marriott, K., Stuckey, P., Tam, V., He, W.: Removing node overlapping in graph layout using constrained optimization. Constraints 8, 143–171 (2003)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Dwyer, T., Marriott, K., Stuckey, P.J.: Fast node overlap removal. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 153–164. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Goldfarb, D., Idnani, A.: A numerically stable dual method for solving strictly convex quadratic programs. Mathematical Programming 26, 1–33 (1983)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Marriott, K., Sbarski, P., Gelder, T., Prager, D., Bulka, A.: Hi-Trees and Their Layout. IEEE Transactions on Visualization and Computer Graphics (to appear)Google Scholar
  9. 9.
    Sbarski, P., Gelder, T., Marriott, K., Prager, D., Bulka, A.: Visualizing Argument Structure. In: Proceedings of the 4th International Symposium on Advances in Visual Computing, pp. 129–138 (2008)Google Scholar
  10. 10.
    Walker I, J.Q.: A node-positioning algorithm for general trees. Softw. Pract. Exper. 20(7), 685–705 (1990)Google Scholar
  11. 11.
    Reingold, E.M., Tilford, J.S.: Tidier drawings of trees. IEEE Transactions on Software Engineering 7(2), 223–228 (1981)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

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

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