On Embedding a Graph in the Grid with the Maximum Number of Bends and Other Bad Features

  • Giuseppe Di Battista
  • Fabrizio Frati
  • Maurizio Patrignani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4475)


Graph Drawing is (usually) concerned with the production of readable representations of graphs. In this paper, instead of investigating how to produce “good” drawings, we tackle the opposite problem of producing “bad” drawings. In particular, we study how to construct orthogonal drawings with many bends along the edges and with large area. Our results show surprising contact points, in Graph Drawing, between the computational cost of niceness and the one of ugliness.


Plane Graph Maximum Area External Face Internal Face Orthogonal Representation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Di Battista, G., Liotta, G., Vargiu, F.: Spirality and optimal orthogonal drawings. SIAM J. Comput. 27(6), 1764–1811 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bertolazzi, P., Di Battista, G., Didimo, W.: Computing orthogonal drawings with the minimum number of bends. In: Dehne, F., Rau-Chaplin, A., Sack, J.-R., Tamassia, R. (eds.) WADS 1997. LNCS, vol. 1272, pp. 331–344. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  3. 3.
    Bridgeman, S.S., Di Battista, G., Didimo, W., Liotta, G., Tamassia, R., Vismara, L.: Turn-regularity and optimal area drawings of orthogonal representations. Computational Geometry 16, 53–93 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Cairns, G., Nikolayevsky, Y.: Bounds for generalized thrackles. Discrete & Computational Geometry 23(2), 191–206 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing, Upper Saddle River, NJ. Prentice-Hall, Englewood Cliffs (1999)zbMATHGoogle Scholar
  6. 6.
    Fößmeier, U., Kaufmann, M.: Drawing high degree graphs with low bend numbers. In: Brandenburg, F.J. (ed.) GD 1995. LNCS, vol. 1027, pp. 254–266. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  7. 7.
    Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comput. 31(2), 601–625 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Lovász, L., Pach, J., Szegedy, M.: On Conway’s thrackle conjecture. In: Symposium on Computational Geometry, pp. 147–151 (1995)Google Scholar
  9. 9.
    Nakano, S.-I., Yoshikawa, M.: A linear-time algorithm for bend-optimal orthogonal drawings of biconnected cubic plane graphs. In: Marks, J. (ed.) Graph Drawing 2000. LNCS, vol. 1984, pp. 296–307. Springer, Heidelberg (2000)Google Scholar
  10. 10.
    Patrignani, M.: On the complexity of orthogonal compaction. Comput. Geom. 19(1), 47–67 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Rahman, M.S., Nakano, S.-I., Nishizeki, T.: A linear algorithm for bend-optimal orthogonal drawings of triconnected cubic plane graphs. J. Graph Algorithms Appl. 3(4), 31–62 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Tamassia, R.: New layout techniques for entity-relationship diagrams. In: Proc. 4th Internat. Conf. on Entity-Relationship Approach, pp. 304–311 (1985)Google Scholar
  13. 13.
    Tamassia, R.: On embedding a graph in the grid with the minimum number of bends. SIAM J. Comput. 16(3), 421–444 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Tamassia, R., Di Battista, G., Batini, C.: Automatic graph drawing and readability of diagrams. IEEE Trans. Syst. Man. Cybern. SMC-18(1), 61–79 (1988)CrossRefGoogle Scholar
  15. 15.
    Tamassia, R., Tollis, I.G.: Planar grid embedding in linear time. IEEE Trans. Circuits Syst. CAS-36(9), 1230–1234 (1989)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Tamassia, R., Tollis, I.G., Vitter, J.S.: Lower bounds and parallel algorithms for planar orthogonal grid drawings. In: Proc. IEEE Symposium on Parallel and Distributed Processing, pp. 386–393. IEEE Computer Society Press, Los Alamitos (1991)CrossRefGoogle Scholar
  17. 17.
    Vijayan, G., Wigderson, A.: Rectilinear graphs and their embeddings. SIAM J. Comput. 14, 355–372 (1985)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Giuseppe Di Battista
    • 1
  • Fabrizio Frati
    • 1
  • Maurizio Patrignani
    • 1
  1. 1.Dipartimento di Informatica e Automazione – Università di Roma TreItaly

Personalised recommendations