Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Straight-Line Rectangular Drawings of Clustered Graphs

  • Conference paper
Algorithms and Data Structures (WADS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5664))

Included in the following conference series:

  • 1407 Accesses

Abstract

We show that every c-planar clustered graph admits a straight-line c-planar drawing in which each cluster is represented by an axis-parallel rectangle, thus solving a problem posed by Eades, Feng, Lin, and Nagamochi [Algorithmica, 2006].

Fabrizio Frati was partially supported by the Italian Ministry of Research, Grant RBIP06BZW8, project “Advanced tracking system in intermodal freight transportation”. Michael Kaufmann was partially supported by the German Research Foundation (DFG), Grant KA812/13-1, project “Scalable visual analytics”.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Angelini, P., Frati, F., Kaufmann, M.: Straight-line rectangular drawings of clustered graphs. Tech. Report RT-DIA-144-2009, Dept. of Computer Sci., Roma Tre Univ. (2009), http://web.dia.uniroma3.it/ricerca/rapporti/rt/2009-144.pdf

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. 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)

    Chapter  Google Scholar 

  5. Di Battista, G., Drovandi, G., Frati, F.: How to draw a clustered tree. In: Dehne, F., Sack, J.-R., Zeh, N. (eds.) WADS 2007. LNCS, vol. 4619, pp. 89–101. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Eades, P., Feng, Q., Lin, X., Nagamochi, H.: Straight-line drawing algorithms for hierarchical graphs and clustered graphs. Algorithmica 44(1), 1–32 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Eades, P., Feng, Q., Nagamochi, H.: Drawing clustered graphs on an orthogonal grid. J. Graph Alg. Appl. 3(4), 3–29 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. Eades, P., Feng, Q.W., Lin, X.: Straight-line drawing algorithms for hierarchical graphs and clustered graphs. In: North, S.C. (ed.) GD 1996. LNCS, vol. 1190, pp. 113–128. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  9. Fary, I.: On straight line representions of planar graphs. Acta. Sci. Math. 11, 229–233 (1948)

    MATH  Google Scholar 

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

    Google Scholar 

  11. Feng, Q., Cohen, R.F., Eades, P.: How to draw a planar clustered graph. In: Li, M., Du, D.-Z. (eds.) COCOON 1995. LNCS, vol. 959, pp. 21–30. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  12. 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)

    Chapter  Google Scholar 

  13. 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)

    Chapter  Google Scholar 

  14. 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)

    Chapter  Google Scholar 

  15. Jelínková, E., Kára, J., Kratochvíl, J., Pergel, M., Suchý, O., Vyskočil, 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)

    Chapter  Google Scholar 

  16. Jünger, M., Leipert, S., Percan, M.: Triangulating clustered graphs. Technical report, Zentrum für Angewandte Informatik Köln (December 2002)

    Google Scholar 

  17. Nagamochi, H., Kuroya, K.: Drawing c-planar biconnected clustered graphs. Discr. Appl. Math. 155(9), 1155–1174 (2007)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Automazione, Roma Tre University, Italy

    Patrizio Angelini & Fabrizio Frati

  2. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Germany

    Michael Kaufmann

Authors
  1. Patrizio Angelini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fabrizio Frati
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael Kaufmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina Gavrilova

  3. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, P.O. Box, K1S 5B6, Ontario, Canada

    Jörg-Rüdiger Sack

  4. University of Calgary, Calgary, AB, Canada

    Csaba D. Tóth

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Angelini, P., Frati, F., Kaufmann, M. (2009). Straight-Line Rectangular Drawings of Clustered Graphs. In: Dehne, F., Gavrilova, M., Sack, JR., Tóth , C.D. (eds) Algorithms and Data Structures. WADS 2009. Lecture Notes in Computer Science, vol 5664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03367-4_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03367-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03366-7

  • Online ISBN: 978-3-642-03367-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation