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Optimizing Wiggle in Storylines

Authors Alexander Dobler , Tim Hegemann , Martin Nöllenburg , Alexander Wolff

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LIPIcs.GD.2025.39.pdf
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ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Human-centered computing → Graph drawings
Keywords
  • Storyline visualization
  • wiggle minimization
  • NP-complete
  • linear programming
  • quadratic programming
  • experimental analysis

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Abstract

A storyline visualization shows interactions between characters over time. Each character is represented by an x-monotone curve. Time is mapped to the x-axis, and groups of characters that interact at a particular point t in time must be ordered consecutively in the y-dimension at x = t. The predominant objective in storyline optimization so far has been the minimization of crossings between (blocks of) characters. Building on this work, we investigate another important, but less studied quality criterion, namely the minimization of wiggle, i.e., the amount of vertical movement of the characters over time. 
Given a storyline instance together with an ordering of the characters at any point in time, we show that wiggle count minimization is NP-complete. In contrast, we provide algorithms based on mathematical programming to solve linear wiggle height minimization and quadratic wiggle height minimization efficiently. Finally, we introduce a new method for routing character curves that focuses on keeping distances between neighboring curves constant as long as they run in parallel.
We have implemented our algorithms, and we conduct a case study that explores the differences between the three optimization objectives. We use existing benchmark data, but we also present a new use case for storylines, namely the visualization of rolling stock schedules in railway operation.

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Alexander Dobler, Tim Hegemann, Martin Nöllenburg, and Alexander Wolff. Optimizing Wiggle in Storylines. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.GD.2025.39

Author Details

Alexander Dobler
  • TU Wien, Austria
Tim Hegemann
  • Universität Würzburg, Germany
Martin Nöllenburg
  • TU Wien, Austria
Alexander Wolff
  • Universität Würzburg, Germany

Funding

  • Dobler, Alexander: Vienna Science and Technology Fund (WWTF) grant [10.47379/ICT19035].
  • Hegemann, Tim: Federal Ministry of Research, Technology and Space (BMFTR) grant [01IS22012C].
  • Nöllenburg, Martin: Vienna Science and Technology Fund (WWTF) grant [10.47379/ICT19035].

Acknowledgements

We thank Marie Schmidt for discovering the similarities between Storylines and Rolling Stock Schedules. We thank Rowan Hoogervorst and Boris Grimm for providing the Rolling Stock Schedules dataset and for their helpful feedback.

Supplementary Materials

References

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