Abstract
The Kandinsky model has been introduced by Fößmeier and Kaufmann in order to deal with planar orthogonal drawings of planar graphs with maximal vertex degree higher than four [7]. No polynomial-time algorithm is known for computing a (region preserving) bend minimal Kandinsky drawing. In this paper we suggest a new 2-approximation algorithm for this problem. Our extensive computational experiments [13] show that the quality of the computed solutions is better than those of its predecessors [6]. E.g., for all instances in the Rome graph benchmark library [4] it computed the optimal solution, and for randomly generated triangulated graphs with up to 800 vertices, the absolute error was less than 2 on average.
Full paper, submitted to GD 2006.
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
AGD User Manual (1999), http://www.ads.tuwien.ac.at/AGD/
Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows. Prentice-Hall, Englewood Cliffs (1993)
Batini, C., Nardelli, E., Tamassia, R.: A Layout Algorithm for Data Flow Diagrams. IEEE Trans. Softw. Eng (SE) 12(4), 538–546 (1986)
Di Battista, G., Garg, A., Liotta, G., Tamassia, R., Tassinari, E., Vargiu, F.: An Experimental Comparison of Three Graph Drawing Algorithms. In: Proc. 11th Ann. ACM Symp. Comput. Geom., pp. 306–315. ACM Press, New York (1995)
Bertolazzi, P., Di Battista, G., Didimo, W.: Computing orthogonal drawings with the minimum number of bends. IEEE Trans. Comput. 49(8), 826–840 (2000)
Eiglsperger, M.: Automatic Layout of UML Calss Diagrams: A Topology-Shape-Metrics Approach. PhD thesis, Eberhard-Karls-Universität zu Tübingen (2003)
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)
Fößmeier, U.: Orthogonale Visualisierungstechnicken für Graphen. PhD thesis, Eberhard-Karls-Universitä t zu Tübingen (1997)
Fößmeier, U., Kaufmann, M.: Algorithms and Area Bounds for Nonplanar Orthogonal Drawings. In: DiBattista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 134–145. Springer, Heidelberg (1997)
Garg, A., Tamassia, R.: A New Minimum Cost Flow Algorithm with Applications to Graph Drawing. In: North, S.C. (ed.) GD 1996. LNCS, vol. 1190, pp. 201–216. Springer, Heidelberg (1997)
ILOG CPLEX 8.1: http://www.ilog.com/products/cplex/
Tamassia, R.: On embedding a graph in the grid with the minimum number of bends. SIAM Journal on Computing 16(3), 421–444 (1987)
Yildiz, C.: Knickminimales Orthogonales Zeichnen Planarer Graphen im Kandinsky Modell. PhD thesis, Vienna University of Technology (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Barth, W., Mutzel, P., Yıldız, C. (2007). A New Approximation Algorithm for Bend Minimization in the Kandinsky Model. In: Kaufmann, M., Wagner, D. (eds) Graph Drawing. GD 2006. Lecture Notes in Computer Science, vol 4372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70904-6_33
Download citation
DOI: https://doi.org/10.1007/978-3-540-70904-6_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70903-9
Online ISBN: 978-3-540-70904-6
eBook Packages: Computer ScienceComputer Science (R0)