Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.11952 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916141444628480 |
|---|---|
| author | Katheder, Julia Kobourov, Stephen G. Kuckuk, Axel Pfister, Maximilian Zink, Johannes |
| author_facet | Katheder, Julia Kobourov, Stephen G. Kuckuk, Axel Pfister, Maximilian Zink, Johannes |
| contents | We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to permute the vertices on the other layers (respecting the given tree embeddings) in order to minimize the number of crossings. While this problem is known to be NP-hard for multiple trees even on just two layers, we describe a dynamic program running in polynomial time for the restricted case of two trees. If there are more than two trees, we restrict the number of layers to three, which allows for a reduction to a shortest-path problem. This way, we achieve XP-time in the number of trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_11952 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Simultaneous Drawing of Layered Trees Katheder, Julia Kobourov, Stephen G. Kuckuk, Axel Pfister, Maximilian Zink, Johannes Discrete Mathematics Data Structures and Algorithms We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to permute the vertices on the other layers (respecting the given tree embeddings) in order to minimize the number of crossings. While this problem is known to be NP-hard for multiple trees even on just two layers, we describe a dynamic program running in polynomial time for the restricted case of two trees. If there are more than two trees, we restrict the number of layers to three, which allows for a reduction to a shortest-path problem. This way, we achieve XP-time in the number of trees. |
| title | Simultaneous Drawing of Layered Trees |
| topic | Discrete Mathematics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2302.11952 |