Revisiting ILP Models for Exact Crossing Minimization in Storyline Drawings
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909305006981120 |
|---|---|
| author | Dobler, Alexander Jünger, Michael Jünger, Paul J. Meffert, Julian Mutzel, Petra Nöllenburg, Martin |
| author_facet | Dobler, Alexander Jünger, Michael Jünger, Paul J. Meffert, Julian Mutzel, Petra Nöllenburg, Martin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02858 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisiting ILP Models for Exact Crossing Minimization in Storyline Drawings Dobler, Alexander Jünger, Michael Jünger, Paul J. Meffert, Julian Mutzel, Petra Nöllenburg, Martin Data Structures and Algorithms Computational Geometry 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. |
| title | Revisiting ILP Models for Exact Crossing Minimization in Storyline Drawings |
| topic | Data Structures and Algorithms Computational Geometry |
| url | https://arxiv.org/abs/2409.02858 |