Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Approximation and Online Algorithms

WAOA 2012: Approximation and Online Algorithms pp 272–285Cite as

A 4-Approximation for the Height of Drawing 2-Connected Outer-Planar Graphs

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7846))

Abstract

A graph drawing algorithm aims to create a picture of the graph, usually with vertices drawn at grid points while keeping the grid-size small. Many algorithms are known that create planar drawings of planar graphs, but most of them bound the height of the drawing in terms of the number of vertices. In this paper, we give an algorithm that draws 2-connected outer-planar graphs such that the height is a 4-approximation of the optimal height.

Research partially supported by NSERC and by the Ross and Muriel Cheriton Fellowship.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Biedl, T.: Drawing outer-planar graphs in O(nlogn) area. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 54–65. Springer, Heidelberg (2002), Full-length version appeared in [2]

    Chapter  Google Scholar 

  2. Biedl, T.: Small drawings of outerplanar graphs, series-parallel graphs, and other planar graphs. Discrete and Computational Geometry 45(1), 141–160 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bodlaender, H.L., Fomin, F.V.: Approximation of pathwidth of outerplanar graphs. Journal of Algorithms 43(2), 190–200 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Brandenburg, F.-J.: Drawing planar graphs on (8/9)*n2 area. Electronic Notes in Discrete Mathematics 31, 37–40 (2008)

    Article  MathSciNet  Google Scholar 

  5. Chrobak, M., Nakano, S.-I.: Minimum-width grid drawings of plane graphs. Comput. Geom. 11(1), 29–54 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Di Battista, G., Frati, F.: Small area drawings of outerplanar graphs. Algorithmica 54(1), 25–53 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Dujmovic, V., Fellows, M., Kitching, M., Liotta, G., McCartin, C., Nishimura, N., Ragde, P., Rosamond, F., Whitesides, S., Wood, D.: On the parameterized complexity of layered graph drawing. Algorithmica 52, 267–292 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Felsner, S., Liotta, G., Wismath, S.: Straight-line drawings on restricted integer grids in two and three dimensions. Journal of Graph Algorithms and Applications 7(4), 335–362 (2003)

    Article  MathSciNet  Google Scholar 

  9. Formann, M., Wagner, F.: The VLSI layout problem in various embedding models. In: Möhring, R.H. (ed.) WG 1990. LNCS, vol. 484, pp. 130–139. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  10. Frati, F.: Straight-line drawings of outerplanar graphs in O(dn log n) area. In: Canadian Conference on Computational Geometry (CCCG 2007), pp. 225–228 (2007)

    Google Scholar 

  11. Frati, F.: Lower bounds on the area requirements of series-parallel graphs. Discrete Mathematics & Theoretical Computer Science 12(5), 139–174 (2010)

    MathSciNet  Google Scholar 

  12. de Fraysseix, H., Pach, J., Pollack, R.: Small sets supporting Fary embeddings of planar graphs. In: ACM Symposium on Theory of Computing (STOC 1988), pp. 426–433 (1988)

    Google Scholar 

  13. de 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 

  14. Garg, A., Rusu, A.: Area-efficient planar straight-line drawings of outerplanar graphs. Discrete Applied Mathematics 155(9), 1116–1140 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Heath, L.S., Rosenberg, A.L.: Laying out graphs using queues. SIAM Journal on Computing 21(5), 927–958 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  16. Krug, M., Wagner, D.: Minimizing the area for planar straight-line grid drawings. In: Hong, S.-H., Nishizeki, T., Quan, W. (eds.) GD 2007. LNCS, vol. 4875, pp. 207–212. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  17. Mondal, D., Alam, M.J., Rahman, M. S.: Minimum-layer drawings of trees. In: Katoh, N., Kumar, A. (eds.) WALCOM 2011. LNCS, vol. 6552, pp. 221–232. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  18. Mondal, D., Nishat, R.I., Rahman, M.S., Alam, M.J.: Minimum-area drawings of plane 3-trees. J. Graph Algorithms Appl. 15(2), 177–204 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Scheffler, P.: A linear-time algorithm for the pathwidth of trees. In: Bodendieck, R., Henn, R. (eds.) Topics in Combinatorics and Graph Theory, pp. 613–620. Physica-Verlag, Heidelberg (1990)

    Chapter  Google Scholar 

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

    Google Scholar 

  21. Suderman, M.: Pathwidth and layered drawings of trees. International Journal of Computational Geometry and Applications 14(3), 203–225 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  22. Tayu, S., Nomura, K., Ueno, S.: On the two-dimensional orthogonal drawing of series-parallel graphs. Discrete Applied Mathematics 157(8), 1885–1895 (2009)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Therese Biedl

Authors
  1. Therese Biedl
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Thomas Erlebach

  2. Dipartimento di Informatica "Renato M. Capocelli", Università di Salerno, Via Ponte Don Melillo, 84081, Fisciano, SA, Italy

    Giuseppe Persiano

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Biedl, T. (2013). A 4-Approximation for the Height of Drawing 2-Connected Outer-Planar Graphs. In: Erlebach, T., Persiano, G. (eds) Approximation and Online Algorithms. WAOA 2012. Lecture Notes in Computer Science, vol 7846. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38016-7_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38016-7_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38015-0

  • Online ISBN: 978-3-642-38016-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation