A Fully Dynamic Algorithm to Test the Upward Planarity of Single-Source Embedded Digraphs

  • Aimal Rextin
  • Patrick Healy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5417)


In this paper, we present a dynamic algorithm that checks if a single-source embedded digraph is upward planar in the presence of edge insertions and edge deletions. Let G φ be an upward planar single-source embedded digraph and let G φ be a single-source embedded digraph obtained by updating G φ . We show that the upward planarity of G φ can be checked in O(logn) amortized time when the external face is fixed.


  1. 1.
    Bender, M.A., Cole, R., Demaine, E.D., Farach-Colton, M., Zito, J.: Two simplified algorithms for maintaining order in a list. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 152–164. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Bertolazzi, P., Battista, G.D., Didimo, W.: Quasi-upward planarity. Algorithmica 32(3), 474–506 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Bertolazzi, P., Battista, G.D., Liotta, G., Mannino, C.: Upward drawings of triconnected digraphs. Algorithmica 12(6), 476–497 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Bertolazzi, P., Battista, G.D., Mannino, C., Tamassia, R.: Optimal upward planarity testing of single-source digraphs. SIAM J. Comput. 27(1), 132–169 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Demetrescu, C., Finocchi, I., Italiano, G.: Handbook of Graph Theory. In: Yellen, J., Gross, J.L. (eds.) Dynamic Graph Algorithms. CRC Press Series, in Discrete Mathematics and Its Applications, vol. 10.2 (2003) ISBN 1-58488-090-2Google Scholar
  6. 6.
    Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice-Hall, Englewood Cliffs (1999)zbMATHGoogle Scholar
  7. 7.
    Didimo, W.: Computing upward planar drawings using switch-regularity heuristics. In: SOFSEM, pp. 117–126 (2005)Google Scholar
  8. 8.
    Didimo, W., Giordano, F., Liotta, G.: Upward spirality and upward planarity testing. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 117–128. Springer, Heidelberg (2006)CrossRefGoogle 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)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Hutton, M.D., Lubiw, A.: Upward planar drawing of single-source acyclic digraphs. SIAM J. Comput. 25(2), 291–311 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Papakostas, A.: Upward planarity testing of outerplanar DAGs. In: Proceedings Graph Drawing. pp. 298–306 (1994)Google Scholar
  12. 12.
    Tamassia, R.: On-line planar graph embedding. J. Algorithms 21(2), 201–239 (1996)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Aimal Rextin
    • 1
  • Patrick Healy
    • 1
  1. 1.Computer Science DepartmentUniversity of LimerickIreland

Personalised recommendations