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Rolling Upward Planarity Testing of Strongly Connected Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8165))

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Abstract

A graph is upward planar if it can be drawn without edge crossings such that all edges point upward. Upward planar graphs have been studied on the plane, the standing and rolling cylinders. For all these surfaces, the respective decision problem \(\mathcal{NP}\)-hard in general. Efficient testing algorithms exist if the graph contains a single source and a single sink but only for the plane and standing cylinder.

Here we show that there is a linear-time algorithm to test whether a strongly connected graph is upward planar on the rolling cylinder. For our algorithm, we introduce dual and directed SPQR-trees as extensions of SPQR-trees.

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References

  1. Auer, C., Bachmaier, C., Brandenburg, F.J., Gleißner, A., Hanauer, K.: The duals of upward planar graphs on cylinders. In: Golumbic, M.C., Stern, M., Levy, A., Morgenstern, G. (eds.) WG 2012. LNCS, vol. 7551, pp. 103–113. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  2. Auer, C., Bachmaier, C., Brandenburg, F.J., Gleißner, A.: Classification of planar upward embedding. In: van Kreveld, M., Speckmann, B. (eds.) GD 2011. LNCS, vol. 7034, pp. 415–426. Springer, Heidelberg (2011)

    Google Scholar 

  3. Bachmaier, C., Brandenburg, F.J., Brunner, W., Fülöp, R.: Drawing recurrent hierarchies. J. Graph Alg. App. 16(2), 151–198 (2012)

    Article  MATH  Google Scholar 

  4. Bang-Jensen, J., Gutin, G.: Digraphs: Theory, Algorithms and Applications, 1st edn. Springer (2000)

    Google Scholar 

  5. Bertolazzi, P., Battista, G.D., Mannino, C., Tamassia, R.: Optimal upward planarity testing of single-source digraphs. SIAM J. Comput. 27(1), 132–169 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Brandenburg, F.J.: On the curve complexity of upward planar drawings. In: Mestre, J. (ed.) Computing: The Australasian Theory Symposium, CATS 2012. CRPIT, vol. 128, pp. 27–36. Australian Computer Society (2012)

    Google Scholar 

  7. Brandenburg, F.J.: Upward planar drawings on the standing and the rolling cylinders. Comput. Geom. Theory Appl. (to appear, 2013)

    Google Scholar 

  8. Di Battista, G., Tamassia, R.: Algorithms for plane representations of acyclic digraphs. Theor. Comput. Sci. 61(2-3), 175–198 (1988)

    Article  MATH  Google Scholar 

  9. Di Battista, G., Tamassia, R.: On-line planarity testing. SIAM J. Comput. 25(5), 956–997 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  10. Dolati, A., Hashemi, S.M.: On the sphericity testing of single source digraphs. Discrete Math. 308(11), 2175–2181 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Foldes, S., Rival, I., Urrutia, J.: Light sources, obstructions and spherical orders. Discrete Math. 102(1), 13–23 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  12. Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comput. 31(2), 601–625 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  13. Gutwenger, C., Mutzel, P.: A linear time implementation of SPQR-trees. In: Marks, J. (ed.) GD 2000. LNCS, vol. 1984, pp. 77–90. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  14. Hansen, K.A.: Constant width planar computation characterizes ACC0. Theor. Comput. Sci. 39(1), 79–92 (2006)

    MATH  Google Scholar 

  15. Harary, F., Schwenk, A.J.: The number of caterpillars. Discrete Math. 6(4), 359–365 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hashemi, S.M., Rival, I., Kisielewicz, A.: The complexity of upward drawings on spheres. Order 14, 327–363 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hashemi, S.M.: Digraph embedding. Discrete Math. 233(1-3), 321–328 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Kelly, D.: Fundamentals of planar ordered sets. Discrete Math. 63, 197–216 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  19. Limaye, N., Mahajan, M., Sarma M.N., J.: Evaluating monotone circuits on cylinders, planes and tori. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 660–671. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  20. Limaye, N., Mahajan, M., Sarma, J.M.N.: Upper bounds for monotone planar circuit value and variants. Comput. Complex. 18(3), 377–412 (2009)

    Article  MATH  Google Scholar 

  21. Mohar, B., Thomassen, C.: Graphs on Surfaces. Johns Hopkins Series in the Mathematical Sciences. Johns Hopkins University Press, Baltimore (2001)

    MATH  Google Scholar 

  22. Sugiyama, K., Tagawa, S., Toda, M.: Methods for visual understanding of hierarchical system structures. IEEE-SMC 11(2), 109–125 (1981)

    MathSciNet  Google Scholar 

  23. Thomassen, C.: Planar acyclic oriented graphs. Order 5(1), 349–361 (1989)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. University of Passau, Germany

    Christopher Auer, Christian Bachmaier, Franz J. Brandenburg & Kathrin Hanauer

Authors
  1. Christopher Auer
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  2. Christian Bachmaier
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  3. Franz J. Brandenburg
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  4. Kathrin Hanauer
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Editor information

Editors and Affiliations

  1. Institute of Computer Science, University of Rostock, Albert-Einstein-Straße 22, 18059, Rostock, Germany

    Andreas Brandstädt

  2. Department of Computer Science, University of Kiel, Olshausenstraße 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Institute of Theoretical Computer Science, University of Lübeck, Ratzeburger Allee 160, 23538, Lübeck, Germany

    Rüdiger Reischuk

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Auer, C., Bachmaier, C., Brandenburg, F.J., Hanauer, K. (2013). Rolling Upward Planarity Testing of Strongly Connected Graphs. In: Brandstädt, A., Jansen, K., Reischuk, R. (eds) Graph-Theoretic Concepts in Computer Science. WG 2013. Lecture Notes in Computer Science, vol 8165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45043-3_5

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  • DOI: https://doi.org/10.1007/978-3-642-45043-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45042-6

  • Online ISBN: 978-3-642-45043-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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