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Revisiting ILP Models for Exact Crossing Minimization in Storyline Drawings

Authors Alexander Dobler , Michael Jünger, Paul J. Jünger, Julian Meffert , Petra Mutzel , Martin Nöllenburg

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Author Details

Alexander Dobler
  • TU Wien, Austria
Michael Jünger
  • University of Cologne, Germany
Paul J. Jünger
  • University of Bonn, Germany
Julian Meffert
  • University of Bonn, Germany
Petra Mutzel
  • University of Bonn, Germany
Martin Nöllenburg
  • TU Wien, Austria

Funding

  • Dobler, Alexander: Vienna Science and Technology Fund (WWTF) grant [10.47379/ ICT19035].
  • Meffert, Julian: Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 459420781.
  • Mutzel, Petra: partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 459420781.
  • Nöllenburg, Martin: Vienna Science and Technology Fund (WWTF) grant [10.47379/ICT19035].

Cite AsGet BibTex

Alexander Dobler, Michael Jünger, Paul J. Jünger, Julian Meffert, Petra Mutzel, and Martin Nöllenburg. Revisiting ILP Models for Exact Crossing Minimization in Storyline Drawings. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.GD.2024.31

Abstract

Storyline drawings are a popular visualization of interactions of a set of characters over time, e.g., to show participants of scenes in a book or movie. Characters are represented as x-monotone curves that converge vertically for interactions and diverge otherwise. Combinatorially, the task of computing storyline drawings reduces to finding a sequence of permutations of the character curves for the different time points, with the primary objective being crossing minimization of the induced character trajectories. In this paper, we revisit exact integer linear programming (ILP) approaches for this NP-hard problem. By enriching previous formulations with additional problem-specific insights and new heuristics, we obtain exact solutions for an extended new benchmark set of larger and more complex instances than had been used before. Our experiments show that our enriched formulations lead to better performing algorithms when compared to state-of-the–art modelling techniques. In particular, our best algorithms are on average 2.6-3.2 times faster than the state-of-the-art and succeed in solving complex instances that could not be solved before within the given time limit. Further, we show in an ablation study that our enrichment components contribute considerably to the performance of the new ILP formulation.

Subject Classification

ACM Subject Classification
  • Human-centered computing → Graph drawings
  • Mathematics of computing → Integer programming
  • Mathematics of computing → Permutations and combinations
Keywords
  • Storyline drawing
  • crossing minimization
  • integer linear programming
  • algorithm engineering
  • computational experiments

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References

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