Upward Spirality and Upward Planarity Testing

  • Walter Didimo
  • Francesco Giordano
  • Giuseppe Liotta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3843)

Abstract

The upward planarity testing problem is known to be NP-hard. We describe an O(n4)-time upward planarity testing and embedding algorithm for the class of digraphs that do not contain rigid triconnected components. We also present a new FPT algorithm that solves the upward planarity testing and embedding problem for general digraphs.

References

  1. 1.
    Bertolazzi, P., Battista, G.D., Liotta, G., Mannino, C.: Upward drawings of triconnected digraphs. Algorithmica 6(12), 476–497 (1994)CrossRefGoogle Scholar
  2. 2.
    Bertolazzi, P., Di Battista, G., Didimo, W.: Quasi-upward planarity. Algorithmica 32(3), 474–506 (2002)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bertolazzi, P., Di Battista, G., Mannino, C., Tamassia, R.: Optimal upward planarity testing of single-source digraphs. SIAM J. Comput. 27, 132–169 (1998)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Chan, H.: A parameterized algorithm for upward planarity testing. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 157–168. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing. Prentice-Hall, Upper Saddle River (1999)MATHGoogle Scholar
  6. 6.
    Di Battista, G., Liotta, G., Vargiu, F.: Spirality and optimal orthogonal drawings. SIAM J. Comput. 27(6), 275–298 (1998)Google Scholar
  7. 7.
    Di Battista, G., Tamassia, R.: On-line planarity testing. SIAM J. Comput. 25, 956–997 (1996)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Didimo, W., Giordano, F., Liotta, G.: Upward spirality and upward planarity testing. Technical report. RT-006-05, DIEI - Universitá di Perugia, Italy (2005)Google Scholar
  9. 9.
    Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comput. 31(2), 601–625 (2001)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Healy, P., Lynch, K.: Building blocks of upward planar digraphs. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 296–306. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Healy, P., Lynch, K.: Building blocks of upward planar digraphs. Technical report, TR UL-CSIS-05-2 (2005)Google Scholar
  12. 12.
    Healy, P., Lynch, K.: Fixed-parameter tractable algorithms for testing upward planarity. In: Vojtáš, P., Bieliková, M., Charron-Bost, B., Sýkora, O. (eds.) SOFSEM 2005. LNCS, vol. 3381, pp. 199–208. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  13. 13.
    Hutton, M.D., Lubiw, A.: Upward planarity testing of single-source acyclic digraphs. SIAM J. Comput. 25(2), 291–311 (1996)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Papakostas, A.: Upward planarity testing of outerplanar dags. In: Tamassia, R., Tollis, I.G. (eds.) GD 1994. LNCS, vol. 894, pp. 7298–7306. Springer, Heidelberg (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Walter Didimo
    • 1
  • Francesco Giordano
    • 1
  • Giuseppe Liotta
    • 1
  1. 1.Università di PerugiaItaly

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