Fast and Stronger Lower Bounds for Planar Euclidean Shortest Paths
Abstract
We consider the problem of quickly providing strong lower bounds for the planar Euclidean shortest path (ESP) problem. Such lower bounds are crucial for guiding the search in A* type approaches or for proving quality guarantees for algorithms that compute approximate solutions. Our contributions are two-fold: we show how to simplify ESP instances such that computing and storing a visibility graph becomes feasible while distances within the simplified instance are guaranteed to constitute lower bounds for the original problem instance. Furthermore we show how to precompute a space efficient data structure that allows to perform distance queries on visibility graphs within few microseconds with negligible space overhead.
Cite
Text
Funke et al. "Fast and Stronger Lower Bounds for Planar Euclidean Shortest Paths." International Joint Conference on Artificial Intelligence, 2025. doi:10.24963/IJCAI.2025/946Markdown
[Funke et al. "Fast and Stronger Lower Bounds for Planar Euclidean Shortest Paths." International Joint Conference on Artificial Intelligence, 2025.](https://mlanthology.org/ijcai/2025/funke2025ijcai-fast/) doi:10.24963/IJCAI.2025/946BibTeX
@inproceedings{funke2025ijcai-fast,
title = {{Fast and Stronger Lower Bounds for Planar Euclidean Shortest Paths}},
author = {Funke, Stefan and Koch, Daniel and Proissl, Claudius and Staib, Christian and Weitbrecht, Felix},
booktitle = {International Joint Conference on Artificial Intelligence},
year = {2025},
pages = {8510-8517},
doi = {10.24963/IJCAI.2025/946},
url = {https://mlanthology.org/ijcai/2025/funke2025ijcai-fast/}
}