Abstract
We consider the problem of minimizing the number of bends in an orthogonal planar graph drawing. While the problem can be solved via network flow for a given planar embedding of a graph G, it is NP-hard if we consider the set of all planar embeddings of G. Our approach combines an integer linear programming (ILP) formulation for the set of all embeddings of a planar graph with the network flow formulation for fixed embeddings. We report on computational experiments on a benchmark set containing hard problem instances that was already used for testing the performance of a previously published branch & bound algorithm for solving the same problem. Our new algorithm is about twice as fast as the branch & bound approach for the graphs of the benchmark set.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P. Bertolazzi, G. Di Battista, and W. Didimo. Computing orthogonal drawings with the minimum number of bends. IEEE Transactions on Computers, 49(8):826–840, 2000.
BGL+97._G. Di Battista, A. Garg, G. Liotta, R. Tamassia, E. Tassinari, and F. Vargiu. An experimental comparison of four graph drawing algorithms. Comput. Geom. Theory Appl., 7:303–326, 1997.
D. Bienstock and C. L. Monma. On the complexity of covering vertices by faces in a planar graph. SIAM Journal on Computing, 17(1):53–76, 1988.
D. Bienstock and C. L. Monma. Optimal enclosing regions in planar graphs. Networks, 19(1):79–94, 1989.
D. Bienstock and C. L. Monma. On the complexity of embedding planar graphs to minimize certain distance measures. Algorithmica, 5(1):93–109, 1990.
G. Di Battista and R. Tamassia. On-line planarity testing. SIAM Journal on Computing, 25(5):956–997, 1996.
U. Fößmeier and M. Kaufmann. Drawing high degree graphs with low bend numbers. In F. J. Brandenburg, editor, Graph Drawing (Proc. GD’ 95), volume 1027 of LNCS, pages 254–266. Springer-Verlag, 1996.
C. Gutwenger and P. Mutzel. A linear time implementation of SPQR-trees. In J. Marks, editor, Graph Drawing (Proc. 2000), volume 1984 of LNCS, pages 77–90. Springer-Verlag, 2001.
A. Garg and R. Tamassia. On the computational complexity of upward and rectilinear planarity testing. In R. Tamassia and I. G. Tollis, editors, Proceedings Graph Drawing’ 94, volume 894 of LNCS, pages 286–297. Springer-Verlag, 1994.
J. E. Hopcroft and R. E. Tarjan. Dividing a graph into triconnected components. SIAM Journal on Computing, 2(3):135–158, 1973.
P. Mutzel and R. Weiskircher. Optimizing over all combinatorial embeddings of a planar graph. In G. Cornuéjols, R. Burkard, and G. Wöginger, editors, Proceedings IPCO’ 99, volume 1610 of LNCS, pages 361–376. Springer Verlag, 1999.
P. Mutzel and R. Weiskircher. Computing optimal embeddings for planar graphs. In Proceedings COCOON’ 00, volume 1858 of LNCS, pages 95–104. Springer Verlag, 2000.
R. Tamassia. On embedding a graph in the grid with the minimum number of bends. SIAM Journal on Computing, 16(3):421–444, 1987.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mutzel, P., Weiskircher, R. (2002). Bend Minimization in Orthogonal Drawings Using Integer Programming. In: Ibarra, O.H., Zhang, L. (eds) Computing and Combinatorics. COCOON 2002. Lecture Notes in Computer Science, vol 2387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45655-4_52
Download citation
DOI: https://doi.org/10.1007/3-540-45655-4_52
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43996-7
Online ISBN: 978-3-540-45655-1
eBook Packages: Springer Book Archive