Block Crossings in Storyline Visualizations

TL;DR

This paper investigates block crossings in storyline visualizations, proving NP-hardness, and offers approximation algorithms, fixed-parameter algorithms, and heuristics for optimizing visual clarity in character encounter diagrams.

Contribution

It introduces the concept of block crossings in storyline visualizations and provides algorithms and heuristics for minimizing them, addressing a new complexity aspect.

Findings

Minimizing block crossings is NP-hard.

Developed a constant-factor approximation for bounded meeting sizes.

Presented fixed-parameter algorithms and a greedy heuristic for meetings of size 2.

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. 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.