On Minimizing Crossings in Storyline Visualizations
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 fixedparameter 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2015
 DOI:
 10.48550/arXiv.1509.00442
 arXiv:
 arXiv:1509.00442
 Bibcode:
 2015arXiv150900442K
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Computational Geometry;
 F.2.2;
 G.2.2
 EPrint:
 6 pages, 4 figures. To appear at the 23rd International Symposium on Graph Drawing and Network Visualization (GD 2015)