Abstract
We propose a two-phase heuristic for crossing reduction in circular layouts. While the first algorithm uses a greedy policy to build a good initial layout, an adaptation of the sifting heuristic for crossing reduction in layered layouts is used for local optimization in the second phase. Both phases are conceptually simpler than previous heuristics, and our extensive experimental results indicate that they also yield fewer crossings. An interesting feature is their straightforward generalization to the weighted case.
Research partially supported by DFG under grants Wa 654/13-2 and Br 2158/1-2.
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Baur, M., Brandes, U.: Crossing reduction in circular layouts. Technical Report 2004-14, Universität Karlsruhe (TH), Fakultät für Informatik (August 2004)
Di Battista, G., Garg, A., Liotta, G., Tamassia, R., Tassinari, E., Vargiu, F.: An experimental comparison of four graph drawing algorithms. Computational Geometry: Theory and Applications 7, 303–326 (1997)
Doğrusöz, U., Madden, B., Madden, P.: Circular layout in the Graph Layout Toolkit. In: North, S.C. (ed.) GD 1996. LNCS, vol. 1190, pp. 92–100. Springer, Heidelberg (1997)
Eades, P., Kelly, D.: Heuristics for reducing crossings in 2-layered networks. Ars Combinatoria 21(A), 89–98 (1986)
Eades, P., Wormald, N.C.: Edge crossings in drawings of bipartite graphs. Algorithmica 11, 379–403 (1994)
He, H., Sýkora, O.: New circular drawing algorithms. Unpublished manuscript
Mäkinen, E.: On circular layouts. International Journal of Computer Mathematics 24, 29–37 (1988)
Masuda, S., Kashiwabara, T., Nakajima, K., Fujisawa, T.: On the NPcompleteness of a computer network layout problem. In: Proc. IEEE Intl. Symp. Circuits and Systems, 292–295 (1987)
Matuszewski, C., Schönfeld, R., Molitor, P.: Using sifting for k-layer straightline crossing minimization. In: Kratochvíl, J. (ed.) GD 1999. LNCS, vol. 1731, pp. 217–224. Springer, Heidelberg (1999)
Mehlhorn, K., Näher, S.: The LEDA Platform of Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (1999)
Mitchell, S.L.: Linear algorithms to recognize outerplanar and maximal outerplanar graphs. Information Processing Letters 9(5), 229–232 (1979)
Rudell, R.: Dynamic variable ordering for ordered binary decision diagrams. In: Proc. IEEE Intl. Conf. Computer Aided Design (ICCAD 1993), pp. 42–47 (1993)
Shahrokhi, F., Sýkora, O., László, L., Székely, A., Vrto, I.: Book embeddings and crossing numbers. In: Mayr, E.W., Schmidt, G., Tinhofer, G. (eds.) WG 1994. LNCS, vol. 903, pp. 256–268. Springer, Heidelberg (1995)
Six, J.M., Tollis, I.G.: Circular drawings of biconnected graphs. In: Goodrich, M.T., McGeoch, C.C. (eds.) ALENEX 1999. LNCS, vol. 1619, pp. 57–73. Springer, Heidelberg (1999)
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Baur, M., Brandes, U. (2004). Crossing Reduction in Circular Layouts. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2004. Lecture Notes in Computer Science, vol 3353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30559-0_28
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DOI: https://doi.org/10.1007/978-3-540-30559-0_28
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