Computing Maximum C-planar Subgraphs

Chimani, Markus and Gutwenger, Carsten and Jansen, Mathias and Klein, Karsten and Mutzel, Petra (2009) Computing Maximum C-planar Subgraphs. In: Graph Drawing 16th International Symposium, GD 2008, September 21- 24, 2008, Heraklion, Crete, Greece , pp. 115-120 (Official URL: http://dx.doi.org/10.1007/978-3-642-00219-9_12).

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Abstract

Deciding c-planarity for a given clustered graph C = (G, T ) is one of the most challenging problems in current graph drawing research. Though it is yet unknown if this problem is solvable in polynomial time, latest research focused on algorithmic approaches for special classes of clustered graphs. In this paper, we introduce an approach to solve the general problem using integer linear programming (ILP) techniques. We give an ILP formulation that also includes the natural generalization of cplanarity testing—the maximum c-planar subgraph problem —and solve this ILP with a branch-and-cut algorithm. Our computational results show that this approach is already successful for many clustered graphs of small to medium sizes and thus can be the foundation of a practically efficient algorithm that integrates further sophisticated ILP techniques.

Item Type:Conference Paper
Additional Information:10.1007/978-3-642-00219-9_12
Classifications:G Algorithms and Complexity > G.350 Clusters
G Algorithms and Complexity > G.840 Planarization
ID Code:901

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References

Chimani, M., Mutzel, P., Schmidt, J.M.: Efficient extraction of multiple kuratowski subdivisions. In: GD ’07. LNCS, vol. 4875, pp. 159–170. Springer, Heidelberg (2008)

Cornelsen, S., Wagner, D.: Completely connected clustered graphs. J. Discrete Algorithms 4(2), 313–323 (2006)

Cortese, P.F., Di Battista, G., Patrignani, M., Pizzonia, M.: Clustering cycles into cycles of clusters. In: GD ’04. LNCS, vol. 3383, pp. 100–110. Springer, Heidelberg (2005)

Dahlhaus, E.: A linear time algorithm to recognize clustered planar graphs and its parallelization. In: LATIN ’98. LNCS, vol. 1380, pp. 239–248.Springer (1998)

Di Battista, G., Didimo, W., Marcandalli, A.: Planarization of clustered graphs. In: GD ’01. LNCS, vol. 2265, pp. 60–74. Springer (2002)

Di Battista, G., Frati, F.: Efficient c-planarity testing for embedded flat clustered graphs with small faces. In: GD ’07. LNCS, vol. 4875, pp. 291–302. Springer, Heidelberg (2008)

Di Battista, G., Garg, A., Liotta, G., Tamassia, R., Tassinari, E., Vargiu, F.: An experimental comparison of four graph drawing algorithms. Comput. Geom. Theory Appl. 7(5-6), 303–325 (1997)

Feng, Q.W., Cohen, R.F., Eades, P.: Planarity for clustered graphs. In: ESA ’95. LNCS, vol. 979, pp. 213–226. Springer, Heidelberg (1995)

Goodrich, M.T., Lueker, G.S., Sun, J.Z.: C-planarity of extrovert clustered graphs. In: GD ’05. LNCS, vol. 3843, pp. 211–222. Springer (2005)

Gutwenger, C., Jünger, M., Leipert, S., Mutzel, P., Percan, M., Weiskircher, R.: ¨ Advances in c-planarity testing of clustered graphs. In: GD ’02. LNCS, vol. 2528, pp. 220–235. Springer (2002)

Jelínková, E., Kára, J., Kratochvíl, J., Pergel, M., Suchý, O., Vyskocil, T.: Clustered planarity: Small clusters in eulerian graphs. In: GD ’07. LNCS, vol. 4875, pp. 303–314. Springer (2007)

Jünger, M., Mutzel, P.: Maximum planar subgraphs and nice embeddings: Practical ¨ layout tools. Algorithmica 16(1), 33–59 (1996)

Jünger, M., Thienel, S.: The ABACUS system for branch-and-cut-and-price algo¨ rithms in integer programming and combinatorial optimization. Software: Practice and Experience 30, 1325–1352 (2000)

Kuratowski, K.: Sur le probl`me des courbes gauches en topologie. Fundamenta e Mathematicae 15, 271–283 (1930)