Fr\'echet Edit Distance
<|reference_start|>Fr\'echet Edit Distance: We define and investigate the Fr\'{e}chet edit distance problem. Given two polygonal curves $\pi$ and $\sigma$ and a threshhold value $\delta>0$, we seek the minimum number of edits to $\sigma$ such that the Fr\'{e}chet distance between the edited $\sigma$ and $\pi$ is at most $\delta$. For the edit operations we consider three cases, namely, deletion of vertices, insertion of vertices, or both. For this basic problem we consider a number of variants. Specifically, we provide polynomial time algorithms for both discrete and continuous Fr\'{e}chet edit distance variants, as well as hardness results for weak Fr\'{e}chet edit distance variants.<|reference_end|>
@article{fox2024fr\'{e}chet,
    title={Fr\'{e}chet Edit Distance},
    author={Emily Fox, Amir Nayyeri, Jonathan James Perry and Benjamin Raichel},
    journal={arXiv preprint arXiv:2403.12878},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.12878},
    primaryClass={cs.CG}
}