Skip to main content
SpringerLink
Log in

Drawing Graphs with Vertices at Specified Positions and Crossings at Large Angles

  • Conference paper
Book cover WALCOM: Algorithms and Computation (WALCOM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7157))

Included in the following conference series:

Abstract

Point-set embeddings and large-angle crossings are two areas of graph drawing that independently have received a lot of attention in the past few years. In this paper, we consider problems in the intersection of these two areas. Given the point-set-embedding scenario, we are interested in how much we gain in terms of computational complexity, curve complexity, and generality if we allow large-angle crossings as compared to the planar case.

We investigate two drawing styles where only bends or both bends and edges must be drawn on an underlying grid. We present various results for drawings with one, two, and three bends per edge.

Part of this research has been presented as a poster at the 19th Int. Symposium on Graph Drawing, Eindhoven, 2011.

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

Access this chapter

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 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arikushi, K., Fulek, R., Keszegh, B., Morić, F., Tóth, C.: Graphs that Admit Right Angle Crossing Drawings. In: WG 2010. LNCS, vol. 6410, pp. 135–146. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  2. Cabello, S.: Planar embeddability of the vertices of a graph using a fixed point set is NP-hard. J. Graph Alg. Appl. 10(2), 353–366 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Di Giacomo, E., Didimo, W., Liotta, G., Meijer, H.: Area, curve complexity, and crossing resolution of non-planar graph drawings. Theory Comput. Syst. 49(3), 565–575 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Di Giacomo, E., Frati, F., Fulek, R., Grilli, L., Krug, M.: Orthogeodesic Point-set Embedding of Trees. In: van Kreveld, M., Speckmann, B. (eds.) GD 2011. LNCS. Springer, Heidelberg (to appear, 2012)

    Google Scholar 

  5. Didimo, W., Eades, P., Liotta, G.: Drawing Graphs with Right Angle Crossings. In: Dehne, F., Gavrilova, M.L., Sack, J.-R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 206–217. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  6. Even, S., Itai, A., Shamir, A.: On the complexity of timetable and multicommodity flow problems. SIAM J. Comput. 5(4), 691–703 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fink, M., Haunert, J.H., Mchedlidze, T., Spoerhase, J., Wolff, A.: Drawing Graphs with Vertices at Specified Positions and Crossings at Large Angles. ArXiv e-print abs/1107.4970v1 (2011)

    Google Scholar 

  8. Goaoc, X., Kratochvíl, J., Okamoto, Y., Shin, C.S., Spillner, A., Wolff, A.: Untangling a planar graph. Discrete Comput. Geom. 42(4), 542–569 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Gritzmann, P., Mohar, B., Pach, J., Pollack, R.: Embedding a planar triangulation with vertices at specified positions. Amer. Math. Mon. 98, 165–166 (1991)

    Article  Google Scholar 

  10. Huang, W., Hong, S.H., Eades, P.: Effects of crossing angles. In: Proc. 7th Int. IEEE Asia-Pacific Symp. Inform. Visual (APVIS 2008), pp. 41–46 (2008)

    Google Scholar 

  11. Katz, B., Krug, M., Rutter, I., Wolff, A.: Manhattan-Geodesic Embedding of Planar Graphs. In: Eppstein, D., Gansner, E.R. (eds.) GD 2009. LNCS, vol. 5849, pp. 207–218. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  12. Kaufmann, M., Wiese, R.: Embedding vertices at points: Few bends suffice for planar graphs. J. Graph Alg. Appl. 6(1), 115–129 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  13. Olariu, S.: An optimal greedy heuristic to color interval graphs. Inform. Process. Lett. 37(1), 21–25 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  14. Pach, J., Wenger, R.: Embedding planar graphs at fixed vertex locations. Graphs Combin. 17(4), 717–728 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  15. Papakostas, A., Tollis, I.G.: Efficient orthogonal drawings of high degree graphs. Algorithmica 26, 100–125 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  16. Raghavan, R., Cohoon, J., Sahni, S.: Single bend wiring. J. Algorithms 7(2), 232–257 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  17. Rendl, F., Woeginger, G.: Reconstructing sets of orthogonal line segments in the plane. Discrete Math. 119, 167–174 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  18. Skulrattanakulchai, S.: 4-edge-coloring graphs of maximum degree 3 in linear time. Inform. Process. Lett. 81(4), 191–195 (2002)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lehrstuhl für Informatik I Universität, Würzburg, Germany

    Martin Fink, Jan-Henrik Haunert, Joachim Spoerhase & Alexander Wolff

  2. Department of Mathematics, National Technical University of Athens, Greece

    Tamara Mchedlidze

Authors
  1. Martin Fink
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jan-Henrik Haunert
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tamara Mchedlidze
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Joachim Spoerhase
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Alexander Wolff
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Graph Drawing and Information Visualization Laboratory, Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology, Bangladesh

    Md. Saidur Rahman

  2. , Faculty of Engineering, Department of Computer Science, Gunma University, 1-5-1 Tenjin-Cho, 376-8515, Kiryu-Shi, Japan

    Shin-ichi Nakano

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fink, M., Haunert, JH., Mchedlidze, T., Spoerhase, J., Wolff, A. (2012). Drawing Graphs with Vertices at Specified Positions and Crossings at Large Angles. In: Rahman, M.S., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2012. Lecture Notes in Computer Science, vol 7157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28076-4_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-28076-4_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28075-7

  • Online ISBN: 978-3-642-28076-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation