Maximum Upward Planar Subgraphs of Embedded Planar Digraphs

  • Carla Binucci
  • Walter Didimo
  • Francesco Giordano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4875)


This paper presents an extensive study on the problem of computing maximum upward planar subgraphs of embedded planar digraphs: Complexity results, algorithms, and experiments are presented. Namely: (i) We prove that the addressed problem is NP-Hard; (ii) A fast heuristic and an exponential-time exact algorithm are described; (iii) A wide experimental analysis is performed to show the effectiveness of our techniques.


Test Suite Outgoing Edge Incoming Edge Planar Embedding Planar Drawing 
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  1. 1.
    Bertolazzi, P., Di Battista, G., Didimo, W.: Quasi-upward planarity. Algorithmica 32(3), 474–506 (2002)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bertolazzi, P., Di Battista, G., Liotta, G., Mannino, C.: Upward drawings of triconnected digraphs. Algorithmica 6(12), 476–497 (1994)CrossRefGoogle 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)Google Scholar
  5. 5.
    Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing. Prentice Hall, Upper Saddle River, NJ (1999)MATHCrossRefGoogle Scholar
  6. 6.
    Di Battista, G., Garg, A., Liotta, G., Tamassia, R., Tassinari, E., Vargiu, F.: An experimental comparison of four graph drawing algorithms. Computational Geometry: Theory and Applications 7, 303–326 (1997)MathSciNetGoogle Scholar
  7. 7.
    Didimo, W.: Upward planar drawings and switch-regularity heuristics. Journal of Graph Algorithms and Applications 10(2), 259–285 (2006)MathSciNetGoogle 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.
    Garey, M.R., Johnson, D.S.: Comput. and Intract. Freeman and Co, San Francisco (1979)Google Scholar
  10. 10.
    Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comput. 31(2), 601–625 (2001)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Healy, P., Lynch, K.: Fixed-parameter tractable algorithms for testing upward planarity. International Journal of Foundations of Computer Science 17(5) (2006)Google Scholar
  12. 12.
    Hutton, M.D., Lubiw, A.: Upward planarity testing of single-source acyclic digraphs. SIAM J. Comput. 25(2), 291–311 (1996)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Lichtenstein, D.: Planar formulae and their uses. SIAM J. Comput. 11(2), 329–343 (1982)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Papakostas, A.: Upward planarity testing of outerplanar dags. In: Tamassia, R., Tollis, I(Y.) G. (eds.) GD 1994. LNCS, vol. 894, pp. 298–306. Springer, Heidelberg (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Carla Binucci
    • 1
  • Walter Didimo
    • 1
  • Francesco Giordano
    • 1
  1. 1.DIEI - Università degli Studi di Perugia 

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