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Drawing Planar Graphs on Points Inside a Polygon

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Mathematical Foundations of Computer Science 2012 (MFCS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7464))

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Abstract

In this paper, we study the problem of drawing a given planar graph such that vertices are at pre-specified points and the entire drawing is inside a given polygon. We give a method that shows that for an n-vertex graph and a k-sided polygon, Θ(kn 2) bends are always sufficient. We also give an example of a graph where Θ(kn 2) bends are necessary for such a drawing.

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References

  1. Bachmaier, C., Brunner, W., König, C.: Cyclic Level Planarity Testing and Embedding. In: Hong, S.-H., Nishizeki, T., Quan, W. (eds.) GD 2007. LNCS, vol. 4875, pp. 50–61. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  2. Badent, M., Di Giacomo, E., Liotta, G.: Drawing colored graphs on colored points. Theoretical Computer Science 408(2-3), 129–142 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chiba, N., Nishizeki, T.: The Hamiltonian cycle problem is linear-time solvable for 4-connected planar graphs. Journal of Algorithms 10(2), 187–211 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  4. Di Giacomo, E., Didimo, W., Liotta, G., Meijer, H., Wismath, S.: Constrained Point-Set Embeddability of Planar Graphs. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 360–371. Springer, Heidelberg (2009), http://dx.doi.org/10.1007/978-3-642-00219-9_35

    Chapter  Google Scholar 

  5. Fary, I.: On straight line representation of planar graphs. Szeged. Sect. Sci. Math. 11, 229–233 (1948)

    MathSciNet  Google Scholar 

  6. Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10, 41–51 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  7. 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 

  8. Kaufmann, M., Wiese, R.: Embedding Vertices at Points: Few Bends Suffice for Planar Graphs. In: Kratochvíl, J. (ed.) GD 1999. LNCS, vol. 1731, pp. 165–174. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  9. Lengauer, T.: Combinatorial Algorithms for Integrated Circuit Layout. Teubner/Wiley & Sons, Stuttgart/Chicester (1990)

    MATH  Google Scholar 

  10. Pach, J., Wenger, R.: Embedding Planar Graphs at Fixed Vertex Locations. In: Whitesides, S.H. (ed.) GD 1998. LNCS, vol. 1547, pp. 263–274. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  11. Schnyder, W.: Embedding planar graphs on the grid. In: ACM-SIAM Symposium on Discrete Algorithms (SODA 1990), pp. 138–148 (1990)

    Google Scholar 

  12. Wagner, K.: Bemerkungen zum Vierfarben Problem. Jahresbericht Deutsch. Math. 46, 26–32 (1936)

    Google Scholar 

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Author information

Authors and Affiliations

  1. David R. Cheriton School of Computer Science, University of Waterloo, Canada

    Therese Biedl

  2. Department of Mathematics, University of Lund, Sweden

    Peter Floderus

Authors
  1. Therese Biedl
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  2. Peter Floderus
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynska Dolina, 84248, Bratislava, Slovakia

    Branislav Rovan

  2. Department of Electronics and Computer Science, University of Southampton, SO17 1BJ, Southampton, UK

    Vladimiro Sassone

  3. Institute of Theoretical Computer Science, ETH Zürich, CAB H 39.2, Universitätstrasse 6, 8092, Zürich, Switzerland

    Peter Widmayer

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© 2012 Springer-Verlag Berlin Heidelberg

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Biedl, T., Floderus, P. (2012). Drawing Planar Graphs on Points Inside a Polygon. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_18

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  • DOI: https://doi.org/10.1007/978-3-642-32589-2_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32588-5

  • Online ISBN: 978-3-642-32589-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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