  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. 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.
