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arXiv · 1509.00442

On Minimizing Crossings in Storyline Visualizations

Irina Kostitsyna·Martin Nöllenburg·Valentin Polishchuk·André Schulz·Darren Strash
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Abstract

In a storyline visualization, we visualize a collection of interacting characters (e.g., in a movie, play, etc.) by $x$-monotone curves that converge for each interaction, and diverge otherwise. Given a storyline with $n$ characters, we show tight lower and upper bounds on the number of crossings required in any storyline visualization for a restricted case. In particular, we show that if (1) each meeting consists of exactly two characters and (2) the meetings can be modeled as a tree, then we can always find a storyline visualization with $O(n\log n)$ crossings. Furthermore, we show that there exist storylines in this restricted case that require $\Omega(n\log n)$ crossings. Lastly, we show that, in the general case, minimizing the number of crossings in a storyline visualization is fixed-parameter tractable, when parameterized on the number of characters $k$. Our algorithm runs in time $O(k!^2k\log k + k!^2m)$, where $m$ is the number of meetings.

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Irina Kostitsyna, Martin Nöllenburg, Valentin Polishchuk, André Schulz, Darren Strash. 2015-09-01. On Minimizing Crossings in Storyline Visualizations. https://doi.org/10.1007/978-3-319-27261-0_16

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