Abstract
We describe a branch-and-bound algorithm for computing an orthogonal grid drawing with the minimum number of bends of a biconnected planar graph. Such algorithm is based on an efficient enumeration schema of the embeddings of a planar graph and on several new methods for computing lower bounds of the number of bends. We experiment such algorithm on a large test suite and compare the results with the state-of-the-art. The experiments show how minimizing the number of bends strongly improves several quality measures of the effectiveness of the drawing. We also present a graphic tool with animation that embodies the algorithm and allows interacting with all the phases of the computation.
Research supported in part by the ESPRIT LTR Project no. 20244 - ALCOM-IT
Preview
Unable to display preview. Download preview PDF.
References
T. Biedl and G. Kant. A better heuristic for orthogonal graph drawings. In Proc. 2nd Annu. European Sympos. Algorithms (ESA '94), volume 855 of Lecture Notes in Computer Science, pages 24–35. Springer-Verlag, 1994.
F. J. Brandenburg, editor. Graph Drawing (Proc. GD '95), volume 1027 of Lecture Notes in Computer Science. Springer-Verlag, 1996.
F. J. Brandenburg, M. Himsolt, and C. Rohrer. An experimental comparison of force-directed and randomized graph drawing algorithms. In F. J. Brandenburg, editor, Graph Drawing (Proc. GD '95), volume 1027 of Lecture Notes in Computer Science, pages 76–87. Springer-Verlag, 1996.
G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis. Algorithms for drawing graphs: an annotated bibliography. Comput. Geom. Theory Appl., 4:235–282, 1994.
G. Di Battista, A. Garg, G. Liotta, R. Tamassia, E. Tassinari, and F. Vargiu. An experimental comparison of three graph drawing algorithms. In Proc. 11th Annu. ACM Sympos. Comput. Geom., pages 306–315,1995.
G. Di Battista, G. Liotta, and F. Vargiu. Spirality of orthogonal representations and optimal drawings of series-parallel graphs and 3-planar graphs. In Proc. Workshop Algorithms Data Struct., volume 709 of Lecture Notes in Computer Science, pages 151–162. Springer-Verlag, 1993.
G. Di Battista and R. Tamassia. On-line maintenance of triconnected components with SPQR-tree s. Algorithmica, 15:302–318, 1996. Preprint: Technical Report CS-92-40, Comput. Sci. Dept., Brown Univ. (1992).
G. Di Battista and R. Tamassia. On-line planarity testing. SIAM J. Comput., to appear. Preprint: Technical Report CS-92-39, Comput. Sci. Dept., Brown Univ. (1992).
S. Even. Graph Algorithms. Computer Science Press, Potomac, Maryland, 1979.
A. Garg and R. Tamassia. On the computational complexity of upward and rectilinear planarity testing. Report CS-94-10, Comput. Sci. Dept., Brown Univ., Providence, RI, 1994.
A. Garg and R. Tamassia. On the computational complexity of upward and rectilinear planarity testing. Submitted to SIAM Journal on Computing, 1995.
M. Himsolt. Comparing and evaluating layout algorithms within GraphEd. J. Visual Lang. Comput., 6(3), 1995. (special issue on Graph Visualization, edited by I. F. Cruz and P. Eades).
J. Hopcroft and R. E. Tarjan. Dividing a graph into triconnected components. SIAM J. Comput., 2:135–158, 1973.
S. Jones, P. Eades, A. Moran, N. Ward, G. Delott, and R. Tamassia. A note on planar graph drawing algorithms. Technical Report 216, Department of Computer Science, University of Queensland, 1991.
M. Jünger and P. Mutzel. Exact and heuristic algorithms for 2-layer straightline crossing minimization. In F. J. Brandenburg, editor, Graph Drawing (Proc. GD '95), volume 1027 of Lecture Notes in Computer Science, pages 337–348. Springer-Verlag, 1996.
K. Mehlhorn and S. Näher. LEDA: a platform for combinatorial and geometric computing. Commun. ACM, 38:96–102, 1995.
T. Nishizeki and N. Chiba. Planar graphs: Theory and algorithms. Ann. Discrete Math., 32, 1988.
A. Papakostas and I. G. Tollis. Improved algorithms and bounds for orthogonal drawings. In R. Tamassia and I. G. Tollis, editors, Graph Drawing (Proc. GD '94), volume 894 of Lecture Notes in Computer Science, pages 40–51. Springer-Verlag, 1995.
R. Tamassia. On embedding a graph in the grid with the minimum number of bends. SIAM J. Comput., 16(3):421–444, 1987.
R. Tamassia, G. Di Battista, and C. Batini. Automatic graph drawing and readability of diagrams. IEEE Trans. Syst. Man Cybern., SMC-18(1):61–79, 1988.
R. Tamassia and I. G. Tollis. A unified approach to visibility representations of planar graphs. Discrete Comput. Geom., 1(4):321–341, 1986.
R. Tamassia and I. G. Tollis. Efficient embedding of planar graphs in linear time. In Proc. IEEE Internat. Sympos. on Circuits and Systems, pages 495–498, 1987.
R. Tamassia and I. G. Tollis, editors. Graph Drawing (Proc. GD '94), volume 894 of Lecture Notes in Computer Science. Springer-Verlag, 1995.
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bertolazzi, P., Di Battista, G., Didimo, W. (1997). Computing orthogonal drawings with the minimum number of bends. In: Dehne, F., Rau-Chaplin, A., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 1997. Lecture Notes in Computer Science, vol 1272. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63307-3_72
Download citation
DOI: https://doi.org/10.1007/3-540-63307-3_72
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63307-5
Online ISBN: 978-3-540-69422-9
eBook Packages: Springer Book Archive