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Geometry Matters in Planar Storyplans

Authors Alexander Dobler , Maximilian Holzmüller, Martin Nöllenburg

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ACM Subject Classification
  • Theory of computation → Computational geometry
  • Mathematics of computing → Graph theory
  • Human-centered computing → Graph drawings
Keywords
  • geometric storyplan
  • planarity
  • straight-line drawing
  • dynamic graph drawing

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Abstract

A storyplan visualizes a graph G = (V,E) as a sequence of 𝓁 frames Γ₁, … , Γ_𝓁, each of which is a drawing of the induced subgraph G[V_i] of a vertex subset V_i ⊆ V. Moreover, each vertex v ∈ V is contained in a single consecutive sequence of frames Γ_i, … , Γ_j, all vertices and edges contained in consecutive frames are drawn identically, and the union of all frames is a drawing of G. In GD 2022, the concept of planar storyplans was introduced, in which each frame must be a planar (topological) drawing. Several (parameterized) complexity results for recognizing graphs that admit a planar storyplan were provided, including NP-hardness. In this paper, we investigate an open question posed in the GD paper and show that the geometric and topological settings of the planar storyplan problem differ: We provide an instance of a graph that admits a planar storyplan, but no planar geometric storyplan, in which each frame is a planar straight-line drawing. Still, by adapting the reduction proof from the topological to the geometric setting, we show that recognizing the graphs that admit planar geometric storyplans remains NP-hard.

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Alexander Dobler, Maximilian Holzmüller, and Martin Nöllenburg. Geometry Matters in Planar Storyplans. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 27:1-27:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.GD.2025.27

Author Details

Alexander Dobler
  • TU Wien, Austria
Maximilian Holzmüller
  • TU Wien, Austria
Martin Nöllenburg
  • TU Wien, Austria

Funding

  • Dobler, Alexander: Vienna Science and Technology Fund (WWTF) grant [10.47379/ICT19035].
  • Nöllenburg, Martin: Vienna Science and Technology Fund (WWTF) grant [10.47379/ICT19035].

References

  1. Fabian Beck, Michael Burch, Stephan Diehl, and Daniel Weiskopf. The state of the art in visualizing dynamic graphs. In Rita Borgo, Ross Maciejewski, and Ivan Viola, editors, EuroVis 2014. Eurographics Association, 2014. URL: https://doi.org/10.2312/eurovisstar.20141174.
  2. Carla Binucci, Ulrik Brandes, Giuseppe Di Battista, Walter Didimo, Marco Gaertler, Pietro Palladino, Maurizio Patrignani, Antonios Symvonis, and Katharina Anna Zweig. Drawing trees in a streaming model. In David Eppstein and Emden R. Gansner, editors, Proc. Graph Drawing and Network Visualization (GD'09), volume 5849 of Lecture Notes in Computer Science, pages 292-303. Springer, 2009. URL: https://doi.org/10.1007/978-3-642-11805-0_28.
  3. Carla Binucci, Ulrik Brandes, Giuseppe Di Battista, Walter Didimo, Marco Gaertler, Pietro Palladino, Maurizio Patrignani, Antonios Symvonis, and Katharina Anna Zweig. Drawing trees in a streaming model. Inf. Process. Lett., 112(11):418-422, 2012. URL: https://doi.org/10.1016/j.ipl.2012.02.011.
  4. Carla Binucci, Emilio Di Giacomo, William J. Lenhart, Giuseppe Liotta, Fabrizio Montecchiani, Martin Nöllenburg, and Antonios Symvonis. On the complexity of the storyplan problem. In Patrizio Angelini and Reinhard von Hanxleden, editors, Proc. Graph Drawing and Network Visualization (GD'22), volume 13764 of Lecture Notes in Computer Science, pages 304-318. Springer, 2022. URL: https://doi.org/10.1007/978-3-031-22203-0_22.
  5. Carla Binucci, Emilio Di Giacomo, William J. Lenhart, Giuseppe Liotta, Fabrizio Montecchiani, Martin Nöllenburg, and Antonios Symvonis. On the complexity of the storyplan problem. J. Comput. Syst. Sci., 139:103466, 2024. URL: https://doi.org/10.1016/J.JCSS.2023.103466.
  6. Manuel Borrazzo, Giordano Da Lozzo, Giuseppe Di Battista, Fabrizio Frati, and Maurizio Patrignani. Graph stories in small area. J. Graph Algorithms Appl., 24(3):269-292, 2020. URL: https://doi.org/10.7155/jgaa.00530.
  7. Manuel Borrazzo, Giordano Da Lozzo, Fabrizio Frati, and Maurizio Patrignani. Graph stories in small area. In Daniel Archambault and Csaba D. Tóth, editors, Proc. Graph Drawing and Network Visualization (GD'19), volume 11904 of Lecture Notes in Computer Science, pages 545-558. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-35802-0_41.
  8. Giordano Da Lozzo and Ignaz Rutter. Planarity of streamed graphs. Theor. Comput. Sci., 799:1-21, 2019. URL: https://doi.org/10.1016/J.TCS.2019.09.029.
  9. Giuseppe Di Battista, Walter Didimo, Luca Grilli, Fabrizio Grosso, Giacomo Ortali, Maurizio Patrignani, and Alessandra Tappini. Small point-sets supporting graph stories. In Patrizio Angelini and Reinhard von Hanxleden, editors, Proc. Graph Drawing and Network Visualization (GD'22), volume 13764 of Lecture Notes in Computer Science, pages 289-303. Springer, 2022. URL: https://doi.org/10.1007/978-3-031-22203-0_21.
  10. Giuseppe Di Battista, Walter Didimo, Luca Grilli, Fabrizio Grosso, Giacomo Ortali, Maurizio Patrignani, and Alessandra Tappini. Small point-sets supporting graph stories. J. Graph Algorithms Appl., 27(8):651-677, 2023. URL: https://doi.org/10.7155/JGAA.00639.
  11. Emilio Di Giacomo, Walter Didimo, Giuseppe Liotta, Fabrizio Montecchiani, and Ioannis G. Tollis. Exploring complex drawings via edge stratification. In Stephen K. Wismath and Alexander Wolff, editors, Proc. Graph Drawing and Network Visualization (GD'13), volume 8242 of Lecture Notes in Computer Science, pages 304-315. Springer, 2013. URL: https://doi.org/10.1007/978-3-319-03841-4_27.
  12. Emilio Di Giacomo, Walter Didimo, Giuseppe Liotta, Fabrizio Montecchiani, and Ioannis G. Tollis. Techniques for edge stratification of complex graph drawings. J. Vis. Lang. Comput., 25(4):533-543, 2014. URL: https://doi.org/10.1016/j.jvlc.2014.05.001.
  13. Alexander Dobler, Maximilian Holzmüller, and Martin Nöllenburg. Geometry matters in planar storyplans. CoRR, abs/2508.12747, 2025. URL: https://arxiv.org/abs/2508.12747.
  14. Jirí Fiala, Oksana Firman, Giuseppe Liotta, Alexander Wolff, and Johannes Zink. Outerplanar and forest storyplans. In Henning Fernau, Serge Gaspers, and Ralf Klasing, editors, Proc. Theory and Practice of Computer Science (SOFSEM'24), volume 14519 of Lecture Notes in Computer Science, pages 211-225. Springer, 2024. URL: https://doi.org/10.1007/978-3-031-52113-3_15.
  15. Michael T. Goodrich and Pawel Pszona. Streamed graph drawing and the file maintenance problem. In Stephen K. Wismath and Alexander Wolff, editors, Proc. Graph Drawing and Network Visualization (GD'13), volume 8242 of Lecture Notes in Computer Science, pages 256-267. Springer, 2013. URL: https://doi.org/10.1007/978-3-319-03841-4_23.
  16. Maximilian Holzmüller. Expanding the planar storyplan problem. Master’s thesis, Technische Universität Wien, 2025. URL: https://repositum.tuwien.at/handle/20.500.12708/213348.
  17. Corinna Vehlow, Fabian Beck, and Daniel Weiskopf. Visualizing dynamic hierarchies in graph sequences. IEEE Trans. Vis. Comput. Graph., 22(10):2343-2357, 2016. URL: https://doi.org/10.1109/TVCG.2015.2507595.
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