Revisiting ILP Models for Exact Crossing Minimization in Storyline Drawings

TL;DR

This paper improves ILP models for exactly minimizing crossings in storyline drawings, enabling solutions for larger, more complex instances with faster algorithms and better performance than previous methods.

Contribution

It introduces enriched ILP formulations with problem-specific insights and heuristics, significantly enhancing solution efficiency and scalability for the crossing minimization problem.

Findings

Enriched ILP formulations outperform previous models.

Algorithms are 2.6-3.2 times faster on average.

Successfully solve larger, more complex instances.

Abstract

Storyline drawings are a popular visualization of interactions of a set of characters over time, e.g., to show participants of scenes in a book or movie. Characters are represented as $x$-monotone curves that converge vertically for interactions and diverge otherwise. Combinatorially, the task of computing storyline drawings reduces to finding a sequence of permutations of the character curves for the different time points, with the primary objective being crossing minimization of the induced character trajectories. In this paper, we revisit exact integer linear programming (ILP) approaches for this NP-hard problem. By enriching previous formulations with additional problem-specific insights and new heuristics, we obtain exact solutions for an extended new benchmark set of larger and more complex instances than had been used before. Our experiments show that our enriched formulations lead to better performing algorithms when compared to state-of-the-art modelling techniques. In particular, our best algorithms are on average 2.6-3.2 times faster than the state-of-the-art and succeed in solving complex instances that could not be solved before within the given time limit. Further, we show in an ablation study that our enrichment components contribute considerably to the performance of the new ILP formulation.