Block Crossings in Storyline Visualizations

Abstract

Storyline visualizations help visualize encounters of the characters in a story over time. Each character is represented by an x-monotone curve that goes from left to right visualizing progression of time. 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. In a block crossing, two blocks of parallel lines intersect each other, which is less distracting than the same number of individual crossings being spread over the drawing. In this paper, we show that minimizing the number of block crossings is NP-hard, even if all meetings are of size 2. For this special case, we present a greedy heuristic, which we evaluate experimentally. We show that the general case is fixed-parameter tractable. Our main results is a constant-factor approximation algorithm for meetings of bounded size. The algorithm is based on (approximately) solving a hyperedge deletion problem on hypergraphs that may be of independent interest.