Block Crossings in Storyline Visualizations

Abstract

Abstract. Storyline visualizations help visualize encounters of the characters in a story over time. Each character is represented by an xmonotone curve that goes from left to right. A meeting is represented by having the characters that participate in the meeting run close together for some time. In order to keep the visual complexity low, rather than just minimizing pairwise crossings of curves, we propose to count block crossings, that is, pairs of intersecting bundles of lines. Our main results are as follows. We show that minimizing the number of block crossings is NP-hard, and we develop, for meetings of bounded size, a constant-factor approximation. We also present two fixed-parameter algorithms and, for meetings of size 2, a greedy heuristic that we evaluate experimentally.

Computing Storyline Visualizations with Few Block Crossings

“…In an earlier paper [3], we introduced the concept of minimizing block crossings for drawing storylines. We showed that block crossing minimization in storylines is NP-hard.…”

“…(This more general problem is clearly NP-hard as well.) Secondly, we have now implemented the exact algorithms of our earlier paper [3], which enables an experimental evaluation and comparison. We see that the new algorithm is able to handle larger realistic instances than our previous algorithms, but that the FPT algorithm also has practical relevance.…”

“…Problem Definition. We generalize the problem statement compared to our previous paper [3] in order to handle the instances used by Gronemann et al [8]. In this more general statement, we support meetings that span a certain amount of time (instead of allowing only instantaneous meetings); thus, meetings can overlap with other meetings.…”

“…Intuitively, a block crossing consists of two sets of locally parallel curves intersecting each other without any further curves in the crossing area [3]. (A formal definition is given below.)…”

Bundled Crossings Revisited

“…Due to the practical effectiveness of this approach, it has quickly been adopted by the InfoVis community [7,13,15,16,22]. However, bundled drawings have only recently attracted study from a theoretical point of view [1,9,11,12].…”