Advertisement

Path-Based Supports for Hypergraphs

  • Ulrik Brandes
  • Sabine Cornelsen
  • Barbara Pampel
  • Arnaud Sallaberry
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)

Abstract

A path-based support of a hypergraph H is a graph with the same vertex set as H in which each hyperedge induces a Hamiltonian subgraph. While it is \(\mathcal N\mathcal P\)-complete to compute a path-based support with the minimum number of edges or to decide whether there is a planar path-based support, we show that a path-based tree support can be computed in polynomial time if it exists.

Keywords

Polynomial Time Inductive Hypothesis Tree Support Hamiltonian Path Planar Support 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Beeri, C., Fagin, R., Maier, D., Yannakakis, M.: On the desirability of acyclic database schemes. Journal of the Association for Computing Mashinery 30(4), 479–513 (1983)CrossRefzbMATHGoogle Scholar
  2. 2.
    Brandes, U., Cornelsen, S., Pampel, B., Sallaberry, A.: Hypergraphs and outerplanarity. In: Iliopoulos, C.S., Smyth, W.F. (eds.) IWOCA 2010. LNCS, vol. 6460, pp. 201–211. Springer, Heidelberg (2010)Google Scholar
  3. 3.
    Buchin, K., van Kreveld, M., Meijer, H., Speckmann, B., Verbeek, K.: On planar supports for hypergraphs. In: Eppstein, D., Gansner, E.R. (eds.) GD 2009. LNCS, vol. 5849, pp. 345–356. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Bujtás, C., Tuza, Z.: Color-bounded hypergraphs, II: Interval hypergraphs and hypertrees. Discrete Mathematics 309, 6391–6401 (2009)CrossRefzbMATHGoogle Scholar
  5. 5.
    Flower, J., Fish, A., Howse, J.: Euler diagram generation. Journal on Visual Languages and Computing 19(6), 675–694 (2008)CrossRefGoogle Scholar
  6. 6.
    Johnson, D.S., Krishnan, S., Chhugani, J., Kumar, S., Venkatasubramanian, S.: Compressing large boolean matrices using reordering techniques. In: Nascimento, M.A., Özsu, M.T., Kossmann, D., Miller, R.J., Blakeley, J.A., Schiefer, K.B. (eds.) Proceedings of the 13th International Conference on Very Large Data Bases (VLDB 2004), pp. 13–23. Morgan Kaufmann, San Francisco (2004)Google Scholar
  7. 7.
    Johnson, D.S., Pollak, H.O.: Hypergraph planarity and the complexity of drawing Venn diagrams. Journal of Graph Theory 11(3), 309–325 (1987)CrossRefzbMATHGoogle Scholar
  8. 8.
    Kaufmann, M., van Kreveld, M., Speckmann, B.: Subdivision drawings of hypergraphs. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 396–407. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Korach, E., Stern, M.: The clustering matroid and the optimal clustering tree. Mathematical Programming, Series B 98, 385–414 (2003)CrossRefzbMATHGoogle Scholar
  10. 10.
    Král’, D., Kratochvíl, J., Voss, H.-J.: Mixed hypercacti. Discrete Mathematics 286, 99–113 (2004)CrossRefzbMATHGoogle Scholar
  11. 11.
    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
  12. 12.
    Simonetto, P., Auber, D., Archambault, D.: Fully automatic visualisation of overlapping sets. Computer Graphics Forum 28(3), 967–974 (2009)CrossRefGoogle Scholar
  13. 13.
    Tarjan, R.E., Yannakakis, M.: Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM Journal on Computing 13(3), 566–579 (1984)CrossRefzbMATHGoogle Scholar
  14. 14.
    Wolff, A.: Drawing subway maps: A survey. Informatik-Forschung und Entwicklung 22, 23–44 (1970)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ulrik Brandes
    • 1
  • Sabine Cornelsen
    • 1
  • Barbara Pampel
    • 1
  • Arnaud Sallaberry
    • 2
  1. 1.Fachbereich Informatik & InformationswissenschaftUniversität KonstanzGermany
  2. 2.CNRS UMR 5800 LaBRI, INRIA Bordeaux - Sud OuestPikkoFrance

Personalised recommendations