On Minimizing Crossings in Storyline Visualizations
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 \(\varOmega (n\log n)\) 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.
We thank the anonymous referees for their helpful comments. This research was initiated at the 2nd International Workshop on Drawing Algorithms for Networks in Changing Environments (DANCE 2015) in Langbroek, the Netherlands, supported by the Netherlands Organisation for Scientific Research (NWO) under project no. 639.023.208. IK is supported in part by the NWO under project no. 639.023.208. VP is supported by grant 2014-03476 from the Sweden’s innovation agency VINNOVA.
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