Advertisement

An Interactive Tool to Explore and Improve the Ply Number of Drawings

  • Niklas Heinsohn
  • Michael Kaufmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10692)

Abstract

Given a straight-line drawing \(\varGamma \) of a graph \(G=(V,E)\), for every vertex v the ply disk \(D_v\) is defined as a disk centered at v where the radius of the disk is half the length of the longest edge incident to v. The ply number of a given drawing is defined as the maximum number of overlapping disks at some point in \(\mathrm {I\!R}^2\). Here we present a tool to explore and evaluate the ply number for graphs with instant visual feedback for the user. We evaluate our methods in comparison to an existing ply computation by De Luca et al. [WALCOM’17]. We are able to reduce the computation time from seconds to milliseconds for given drawings and thereby contribute to further research on the ply topic by providing an efficient tool to examine graphs extensively by user interaction as well as some automatic features to reduce the ply number.

Notes

Acknowledgements

We specially thank the authors of [7] for providing their implementation and data to compare with ours. We also thank Patrizio Angelini, Lukas Bachus, Michael Bekos, and Felice De Luca for helpful discussions.

References

  1. 1.
    Angelini, P., Bekos, M.A., Bruckdorfer, T., Hančl, J., Kaufmann, M., Kobourov, S., Symvonis, A., Valtr, P.: Low ply drawings of trees. In: Hu, Y., Nöllenburg, M. (eds.) GD 2016. LNCS, vol. 9801, pp. 236–248. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-50106-2_19 CrossRefGoogle Scholar
  2. 2.
    Angelini, P., Chaplick, S., De Luca, F., Fiala, J., Hancl, J., Heinsohn, N., Kaufmann, M., Kobourov, S., Kratochvil, J., Valtr, P.: On vertex- and empty-ply proximity drawings. In: Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017) (2017, to appear)Google Scholar
  3. 3.
    Atallah, M.J.: Algorithms and Theory of Computation Handbook. CRC Press, Boca Raton (1999)zbMATHGoogle Scholar
  4. 4.
    Bachus, L.: Ply, University of Tübingen. Bachelor thesis (2016)Google Scholar
  5. 5.
    Brandes, U., Eiglsperger, M., Lerner, J., Pich, C.: Graph markup language (GraphML). In: Tamassia, R. (ed.) Handbook on Graph Drawing and Visualization, pp. 517–541. Chapman and Hall/CRC (2013)Google Scholar
  6. 6.
    Chimani, M., Gutwenger, C., Jünger, M., Klau, G.W., Klein, K., Mutzel, P.: The open graph drawing framework (OGDF). In: Tamassia, R. (ed.) Handbook on Graph Drawing and Visualization, pp. 543–569. Chapman and Hall/CRC (2013)Google Scholar
  7. 7.
    De Luca, F., Di Giacomo, E., Didimo, W., Kobourov, S., Liotta, G.: An experimental study on the ply number of straight-line drawings. In: Poon, S.-H., Rahman, M.S., Yen, H.-C. (eds.) WALCOM 2017. LNCS, vol. 10167, pp. 135–148. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-53925-6_11 CrossRefGoogle Scholar
  8. 8.
    Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice-Hall (1999)Google Scholar
  9. 9.
    Di Giacomo, E., Didimo, W., Hong, S., Kaufmann, M., Kobourov, S.G., Liotta, G., Misue, K., Symvonis, A., Yen, H.: Low ply graph drawing. In: Bourbakis, N.G., Tsihrintzis, G.A., Virvou, M. (eds.) 6th International Conference on Information, Intelligence, Systems and Applications, IISA 2015, Corfu, Greece, 6–8 July 2015, pp. 1–6. IEEE (2015)Google Scholar
  10. 10.
    Eppstein, D., Goodrich, M.T.: Studying (non-planar) road networks through an algorithmic lens. In: Aref, W.G., Mokbel, M.F., Schneider, M. (eds.) 16th ACM SIGSPATIAL International Symposium on Advances in Geographic Information Systems, ACM-GIS 2008, Proceedings, 5–7 November 2008, Irvine, California, USA, p. 16. ACM (2008)Google Scholar
  11. 11.
    Fruchterman, T.M.J., Reingold, E.M.: Graph drawing by force-directed placement. Softw., Pract. Exper. 21(11), 1129–1164 (1991)CrossRefGoogle Scholar
  12. 12.
    Hachul, S., Jünger, M.: Drawing large graphs with a potential-field-based multilevel algorithm. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 285–295. Springer, Heidelberg (2005).  https://doi.org/10.1007/978-3-540-31843-9_29 CrossRefGoogle Scholar
  13. 13.
    Hachul, S., Jünger, M.: Large-graph layout algorithms at work: an experimental study. J. Graph Algorithms Appl. 11(2), 345–369 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Himsolt, M.: GML: A Portable Graph File Format. Universität Passau (1997). http://www.fmi.uni-passau.de/graphlet/gml/gml-tr.html
  15. 15.
    Kobourov, S.G.: Force-directed drawing algorithms. In: Tamassia, R. (ed.) Handbook on Graph Drawing and Visualization, pp. 383–408. Chapman and Hall/CRC (2013)Google Scholar
  16. 16.
    Tamassia, R., Liotta, G.: Graph drawing. In: Goodman, J.E., O’Rourke, J. (eds.) Handbook of Discrete and Computational Geometry, 2nd edn., pp. 1163–1185. Chapman and Hall/CRC (2004)Google Scholar
  17. 17.
    Tommila, M.: A C++ high performance arbitrary precision arithmetic package (2003). http://www.apfloat.org/apfloat/
  18. 18.
    Welzl, E., Di Battista, G., Garg, A., Liotta, G., Tamassia, R., Tassinari, E., Vargiu, F.: An experimental comparison of four graph drawing algorithms. Comput. Geom. 7, 303–325 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Wiese, R., Eiglsperger, M., Kaufmann, M.: yFiles - visualization and automatic layout of graphs. In: Jünger, M., Mutzel, P. (eds.) Graph Drawing Software, pp. 173–191. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-642-18638-7_8 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Wilhelm-Schickhard-Institut für InformatikUniversität TübingenTübingenGermany

Personalised recommendations