Splitting Clusters to Get C-Planarity

Angelini, Patrizio and Frati, Fabrizio and Patrignani, Maurizio (2010) Splitting Clusters to Get C-Planarity. In: Graph Drawing 17th International Symposium, GD 2009, September 22-25, 2009, Chicago, IL, USA , pp. 57-68 (Official URL: http://dx.doi.org/10.1007/978-3-642-11805-0_8).

Full text not available from this repository.

Abstract

In this paper we introduce a generalization of the c-planarity testing problem for clustered graphs. Namely, given a clustered graph, the goal of the S PLIT-C-P LANARITY problem is to split as few clusters as possible in order to make the graph c-planar. Determining whether zero splits are enough coincides with testing c-planarity. We show that S PLIT-C-P LANARITY is NP-complete for c-connected clustered triangulations and for non-c-connected clustered paths and cycles. On the other hand, we present a polynomial-time algorithm for flat c-connected clustered graphs whose underlying graph is a biconnected seriesparallel graph, both in the fixed and in the variable embedding setting, when the splits are assumed to maintain the c-connectivity of the clusters.

Item Type:Conference Paper
Additional Information:10.1007/978-3-642-11805-0_8
Classifications:P Styles > P.180 Cluster
G Algorithms and Complexity > G.490 Embeddings
P Styles > P.540 Planar
G Algorithms and Complexity > G.840 Planarization
ID Code:1062

Repository Staff Only: item control page

References

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

Cortese, P.F., Di Battista, G., Frati, F., Patrignani, M., Pizzonia, M.: C-planarity of cconnected clustered graphs. J. Graph Alg. Appl. 12(2), 225–262 (2008)

Cortese, P.F., Di Battista, G., Patrignani, M., Pizzonia, M.: Clustering cycles into cycles of clusters. J. Graph Alg. Appl. 9(3), 391–413 (2005)

Dahlhaus, E.: A linear time algorithm to recognize clustered graphs and its parallelization. In: Lucchesi, C.L., Moura, A.V. (eds.) LATIN 1998. LNCS, vol. 1380, pp. 239–248. Springer, Heidelberg (1998)

Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice-Hall, Englewood Cliffs (1999)

Di Battista, G., Frati, F.: Efficient c-planarity testing for embedded flat clustered graphs with small faces. In: Hong, S.-H., Nishizeki, T., Quan, W. (eds.) GD 2007. LNCS, vol. 4875, pp. 291–302. Springer, Heidelberg (2008)

Feng, Q.: Algorithms for Drawing Clustered Graphs. Ph.D. thesis, The University of Newcastle, Australia (1997)

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

Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NPCompleteness. W.H. Freeman, New York (1979)

Goodrich, M.T., Lueker, G.S., Sun, J.Z.: C-planarity of extrovert clustered graphs. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 211–222. Springer, Heidelberg (2006)

Gutwenger, C., Jünger, M., Leipert, S., Mutzel, P., Percan, M., Weiskircher, R.: Advances in u c-planarity testing of clustered graphs. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 220–235. Springer, Heidelberg (2002)

Jelinek, V., Jelinkova, E., Kratochvil, J., Lidicky, B.: Clustered planarity: Embedded clustered graphs with two-component clusters. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 121–132. Springer, Heidelberg (2009)

Jelinkova, E., Kara, J., Kratochvil, J., Pergel, M., Suchy, O., Vyskocil, T.: Clustered planarity: Small clusters in eulerian graphs. In: Hong, S.-H., Nishizeki, T., Quan, W. (eds.) GD 2007. LNCS, vol. 4875, pp. 303–314. Springer, Heidelberg (2008)

Nishizeki, T., Chiba, N.: Planar Graphs: Theory and Algorithms. Ann. Discrete Math., vol. 32. North-Holland, Amsterdam (1988)