Abstract
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.
Similar content being viewed by others
References
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.) Proceedings of the 5th Workshop on Algorithms, Data Structures. Lecture Notes in Computer Science, vol. 1272, pp. 331–344. Springer, Berlin (1997)
Bridgeman, S.S., Di Battista, G., Didimo, W., Liotta, G., Tamassia, R., Vismara, L.: Turn-regularity and optimal area drawings of orthogonal representations. Comput. Geom. 16, 53–93 (2000)
Cairns, G., Nikolayevsky, Y.: Bounds for generalized thrackles. Discrete Comput. Geom. 23(2), 191–206 (2000)
Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing. Prentice-Hall, Upper Saddle River (1999)
Di Battista, G., Liotta, G., Vargiu, F.: Spirality and optimal orthogonal drawings. SIAM J. Comput. 27(6), 1764–1811 (1998)
Fößmeier, U., Kaufmann, M.: Drawing high degree graphs with low bend numbers. In: Brandenburg, F.J. (ed.) Graph Drawing (Proc. GD ’95). Lecture Notes in Computer Science, vol. 1027, pp. 254–266. Springer, Berlin (1996)
Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comput. 31(2), 601–625 (2001)
Lovász, L., Pach, J., Szegedy, M.: On Conway’s thrackle conjecture. In: Symposium on Computational Geometry, pp. 147–151 (1995)
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. Lecture Notes in Computer Science, pp. 296–307. Springer, Berlin (2000)
Patrignani, M.: On the complexity of orthogonal compaction. Comput. Geom. 19(1), 47–67 (2001)
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)
Tamassia, R.: New layout techniques for entity-relationship diagrams. In: Proceedings of the 4th International Conference on Entity-Relationship Approach, pp. 304–311 (1985)
Tamassia, R.: On embedding a graph in the grid with the minimum number of bends. SIAM J. Comput. 16(3), 421–444 (1987)
Tamassia, R., Di Battista, G., Batini, C.: Automatic graph drawing and readability of diagrams. IEEE Trans. Syst. Man Cybern. 18(1), 61–79 (1988)
Tamassia, R., Tollis, I.G.: Planar grid embedding in linear time. IEEE Trans. Circuits Syst. 36(9), 1230–1234 (1989)
Tamassia, R., Tollis, I.G., Vitter, J.S.: Lower bounds and parallel algorithms for planar orthogonal grid drawings. In: Proceedings of IEEE Symposium on Parallel and Distributed Processing, pp. 386–393 (1991)
Vijayan, G., Wigderson, A.: Rectilinear graphs and their embeddings. SIAM J. Comput. 14, 355–372 (1985)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Di Battista, G., Frati, F. & Patrignani, M. On Embedding a Graph in the Grid with the Maximum Number of Bends and Other Bad Features. Theory Comput Syst 44, 143–159 (2009). https://doi.org/10.1007/s00224-008-9115-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00224-008-9115-0