Computing Storyline Visualizations with Few Block Crossings

  • Thomas C. van Dijk
  • Fabian LippEmail author
  • Peter Markfelder
  • Alexander Wolff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10692)


Storyline visualizations show the structure of a story, by depicting the interactions of the characters over time. Each character is represented by an x-monotone curve from left to right, and a meeting is represented by having the curves of the participating characters run close together for some time. There have been various approaches to drawing storyline visualizations in an automated way. In order to keep the visual complexity low, rather than minimizing pairwise crossings of curves, we count block crossings, that is, pairs of intersecting bundles of lines.

Partly inspired by the ILP-based approach of Gronemann et al. [GD 2016] for minimizing the number of pairwise crossings, we model the problem as a satisfiability problem (since the straightforward ILP formulation becomes more complicated and harder to solve). Having restricted ourselves to a decision problem, we can apply powerful SAT solvers to find optimal drawings in reasonable time. We compare this SAT-based approach with two exact algorithms for block crossing minimization, using both the benchmark instances of Gronemann et al. and random instances. We show that the SAT approach is suitable for real-world instances and identify cases where the other algorithms are preferable.



We thank Martin Gronemann for providing the input files used in the experiments of [8].


  1. 1.
    Balyo, T., Sanders, P., Sinz, C.: HordeSat: a massively parallel portfolio SAT solver. In: Heule, M., Weaver, S. (eds.) SAT 2015. LNCS, vol. 9340, pp. 156–172. Springer, Cham (2015). CrossRefGoogle Scholar
  2. 2.
    Bekos, M.A., Kaufmann, M., Zielke, C.: The book embedding problem from a SAT-solving perspective. In: Di Giacomo, E., Lubiw, A. (eds.) GD 2015. LNCS, vol. 9411, pp. 125–138. Springer, Cham (2015). CrossRefGoogle Scholar
  3. 3.
    van Dijk, T.C., Fink, M., Fischer, N., Lipp, F., Markfelder, P., Ravsky, A., Suri, S., Wolff, A.: Block crossings in storyline visualizations. J. Graph Algorithms Appl. 21(5), 873–913 (2017). CrossRefzbMATHGoogle Scholar
  4. 4.
    van Dijk, T.C., Lipp, F., Markfelder, P., Wolff, A.: Computing storyline visualizations with few block crossings. arXiv report (2017)
  5. 5.
    Eén, N., Mishchenko, A., Sörensson, N.: Applying logic synthesis for speeding up SAT. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 272–286. Springer, Heidelberg (2007). CrossRefGoogle Scholar
  6. 6.
    Eén, N., Sörensson, N.: MiniSat SAT solver (2003).
  7. 7.
    Gil, L., Flores, P., Silveira, L.M.: PMSat: a parallel version of MiniSAT. J. Satisf. Bool. Model. Comput. 6, 71–98 (2008). MathSciNetzbMATHGoogle Scholar
  8. 8.
    Gronemann, M., Jünger, M., Liers, F., Mambelli, F.: Crossing minimization in storyline visualization. In: Hu, Y., Nöllenburg, M. (eds.) GD 2016. LNCS, vol. 9801, pp. 367–381. Springer, Cham (2016). CrossRefGoogle Scholar
  9. 9.
    Kim, N.W., Card, S.K., Heer, J.: Tracing genealogical data with TimeNets. In: Proceedings of the International Conference on Advanced Visual Interfaces (AVI 2010), pp. 241–248 (2010).
  10. 10.
    Knuth, D.E.: The Art of Computer Programming, Volume 3: Sorting and Searching, 2nd edn. Addison Wesley Longman Publishing Co., Inc., Redwood City (1998)Google Scholar
  11. 11.
    Kostitsyna, I., Nöllenburg, M., Polishchuk, V., Schulz, A., Strash, D.: On minimizing crossings in storyline visualizations. In: Di Giacomo, E., Lubiw, A. (eds.) GD 2015. LNCS, vol. 9411, pp. 192–198. Springer, Cham (2015). CrossRefGoogle Scholar
  12. 12.
    Munroe, R.: Movie narrative charts (2009). Accessed 16 Feb 2017
  13. 13.
    Tanahashi, Y., Ma, K.: Design considerations for optimizing storyline visualizations. IEEE Trans. Vis. Comput. Graph. 18(12), 2679–2688 (2012). CrossRefGoogle Scholar
  14. 14.
    Wertheimer, M.: Untersuchungen zur Lehre von der Gestalt. II. Psychologische Forschung 4(1), 301–350 (1923)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Lehrstuhl für Informatik IUniversität WürzburgWürzburgGermany

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