Advances on Testing C-Planarity of Embedded Flat Clustered Graphs

  • Markus Chimani
  • Giuseppe Di Battista
  • Fabrizio Frati
  • Karsten Klein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8871)

Abstract

We show a polynomial-time algorithm for testing c-planarity of embedded flat clustered graphs with at most two vertices per cluster on each face.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Angelini, P., Di Battista, G., Frati, F., Jelínek, V., Kratochvíl, J., Patrignani, M., Rutter, I.: Testing planarity of partially embedded graphs. In: SODA 2010, pp. 202–221. ACM (2010)Google Scholar
  2. 2.
    Angelini, P., Frati, F., Patrignani, M.: Splitting clusters to get C-planarity. In: Eppstein, D., Gansner, E.R. (eds.) GD 2009. LNCS, vol. 5849, pp. 57–68. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Bertolazzi, P., Di Battista, G., Liotta, G., Mannino, C.: Upward drawings of triconnected digraphs. Algorithmica 12(6), 476–497 (1994)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Chimani, M., Di Battista, G., Frati, F., Klein, K.: Advances on testing c-planarity of embedded flat clustered graphs. CoRR, abs/1408.2595 (2014)Google Scholar
  5. 5.
    Chimani, M., Gutwenger, C., Jansen, M., Klein, K., Mutzel, P.: Computing maximum c-planar subgraphs. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 114–120. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Chimani, M., Klein, K.: Shrinking the search space for clustered planarity. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 90–101. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  7. 7.
    Cornelsen, S., Wagner, D.: Completely connected clustered graphs. J. Discrete Algorithms 4(2), 313–323 (2006)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Cortese, P.F., Di Battista, G., Frati, F., Patrignani, M., Pizzonia, M.: C-planarity of c-connected clustered graphs. J. Graph Algorithms Appl. 12(2), 225–262 (2008)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    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)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Dahlhaus, E.: A linear time algorithm to recognize clustered planar graphs and its parallelization. In: Lucchesi, C.L., Moura, A.V. (eds.) LATIN 1998. LNCS, vol. 1380, pp. 239–248. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  11. 11.
    Di Battista, G., Frati, F.: Efficient c-planarity testing for embedded flat clustered graphs with small faces. J. Graph Alg. Appl. 13(3), 349–378 (2009)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Didimo, W., Giordano, F., Liotta, G.: Overlapping cluster planarity. J. Graph Algorithms Appl. 12(3), 267–291 (2008)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Feng, Q.W., Cohen, R.F., Eades, P.: Planarity for clustered graphs. In: Moore, W., Luk, W. (eds.) FPL 1995. LNCS, vol. 975, pp. 213–226. Springer, Heidelberg (1995)Google Scholar
  14. 14.
    Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM Journal on Computing 31(2), 601–625 (2001)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    Gutwenger, C., Jünger, M., Leipert, S., Mutzel, P., Percan, M., Weiskircher, R.: Advances in 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)CrossRefGoogle Scholar
  17. 17.
    Jelínek, V., Jelínková, E., Kratochvíl, J., Lidický, 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)CrossRefGoogle Scholar
  18. 18.
    Jelínek, V., Suchý, O., Tesař, M., Vyskočil, T.: Clustered planarity: Clusters with few outgoing edges. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 102–113. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Jelínková, E., Kára, J., Kratochvíl, J., Pergel, M., Suchý, O., Vyskocil, T.: Clustered planarity: Small clusters in cycles and Eulerian graphs. J. Graph Alg. Appl. 13(3), 379–422 (2009)CrossRefMATHGoogle Scholar
  20. 20.
    Kratochvíl, J., Lubiw, A., Nesetril, J.: Noncrossing subgraphs in topological layouts. SIAM J. Discrete Math. 4(2), 223–244 (1991)CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    Schaefer, M.: Toward a theory of planarity: Hanani-Tutte and planarity variants. J. Graph Algorithms Appl. 17(4), 367–440 (2013)CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    Schaeffer, S.E.: Graph clustering. Computer Science Review 1(1), 27–64 (2007)CrossRefMATHMathSciNetGoogle Scholar
  23. 23.
    Tamassia, R.: On embedding a graph in the grid with the minimum number of bends. SIAM J. Comput. 16(3), 421–444 (1987)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Markus Chimani
    • 1
  • Giuseppe Di Battista
    • 2
  • Fabrizio Frati
    • 3
  • Karsten Klein
    • 3
  1. 1.Theoretical Computer ScienceUniversity OsnabrückGermany
  2. 2.Dipartimento di IngegneriaUniversity Roma TreItaly
  3. 3.School of Information TechnologiesThe University of SydneyAustralia

Personalised recommendations