Skip to main content

The Effect of Almost-Empty Faces on Planar Kandinsky Drawings

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9125))

Abstract

Inspired by the recently-introduced slanted orthogonal graph drawing model, we introduce and study planar Kandinsky drawings with almost-empty faces (i.e., faces that were forbidden in the classical Kandinsky model).

Based on a recent NP-completeness result for Kandinsky drawings by Bläsius et al., we present and experimentally evaluate (i) an ILP that computes bend-optimal Kandinsky drawings with almost-empty faces, and, (ii) a more efficient heuristic that results in drawings with relatively few bends. Our evaluation shows that the new model, in the presence of many triangular faces, not only improves the number of bends, but also the compactness of the resulting drawings.

This work has been supported by DFG grant Ka\(812/17\)-\(1\).

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

Buying options

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. Barth, W., Mutzel, P., Yıldız, C.: A new approximation algorithm for bend minimization in the kandinsky model. In: Kaufmann, M., Wagner, D. (eds.) GD 2006. LNCS, vol. 4372, pp. 343–354. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  2. Bekos, M.A., Kaufmann, M., Krug, R., Näher, S., Roselli, V.: Slanted orthogonal drawings. In: Wismath, S., Wolff, A. (eds.) GD 2013. LNCS, vol. 8242, pp. 424–435. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  3. Bertolazzi, P., Di Battista, G., Didimo, W.: Computing orthogonal drawings with the minimum number of bends. IEEE Transactions on Computers 49(8), 826–840 (2000)

    Article  Google Scholar 

  4. Bläsius, T., Brückner, G., Rutter, I.: Complexity of higher-degree orthogonal graph embedding in the kandinsky model. In: Schulz, A.S., Wagner, D. (eds.) ESA 2014. LNCS, vol. 8737, pp. 161–172. Springer, Heidelberg (2014)

    Google Scholar 

  5. Chen, D.S., Batson, R.G., Dang, Y.: Applied Integer Programming: Modeling and Solution. Wiley (2010)

    Google Scholar 

  6. Di Battista, G., Didimo, W., Patrignani, M., Pizzonia, M.: Orthogonal and quasi-upward drawings with vertices of prescribed size. In: Kratochvíl, J. (ed.) GD 1999. LNCS, vol. 1731, pp. 297–310. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  7. Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall PTR (1998)

    Google Scholar 

  8. Duncan, C.A., Goodrich, M.T.: Graph drawing and cartography. In: Tamassia, R. (ed.) Handbook of Graph Drawing and Visualization, chap. 7, pp. 223–246. CRC Press (2013)

    Google Scholar 

  9. Eiglsperger, M.: Automatic Layout of UML Class Diagrams: A Topology-Shape-Metrics Approach. Ph.D. thesis, Universität Tübingen (2003)

    Google Scholar 

  10. Eiglsperger, M., Fekete, S.P., Klau, G.W.: Orthogonal Graph Drawing. In: Kaufmann, M., Wagner, D. (eds.) Drawing Graphs. LNCS, vol. 2025, pp. 121–171. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  11. Eiglsperger, M., Fößmeier, U., Kaufmann, M.: Orthogonal graph drawing with constraints. In: Shmoys, D.B. (ed.) Symposium on Discrete Algorithms, pp. 3–11. ACM/SIAM (2000)

    Google Scholar 

  12. Eiglsperger, M., Kaufmann, M.: Fast compaction for orthogonal drawings with vertices of prescribed size. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) GD 2001. LNCS, vol. 2265, pp. 124–138. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  13. Fößmeier, U., Kaufmann, M.: Drawing high degree graphs with low bend numbers. In: Brandenburg, Franz J. (ed.) GD 1995. LNCS, vol. 1027, pp. 254–266. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  14. Gurobi Optimization, I.: Gurobi optimizer reference manual (2014). http://www.gurobi.com

  15. Leiserson, C.E.: Area-efficient graph layouts. In: Foundations of Computer Science, pp. 270–281. IEEE Computer Society (1980)

    Google Scholar 

  16. Tamassia, R.: On embedding a graph in the grid with the minimum number of bends. SIAM Journal of Computing 16(3), 421–444 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  17. Valiant, L.G.: Universality considerations in VLSI circuits. IEEE Transaction on Computers 100(2), 135–140 (1981)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Robert Krug .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Bekos, M.A., Kaufmann, M., Krug, R., Siebenhaller, M. (2015). The Effect of Almost-Empty Faces on Planar Kandinsky Drawings. In: Bampis, E. (eds) Experimental Algorithms. SEA 2015. Lecture Notes in Computer Science(), vol 9125. Springer, Cham. https://doi.org/10.1007/978-3-319-20086-6_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-20086-6_27

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20085-9

  • Online ISBN: 978-3-319-20086-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics