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.

翻译：我们定义并研究了Fréchet编辑距离问题。给定两条多边形曲线$\pi$和$\sigma$以及阈值$\delta>0$，目标是寻找对$\sigma$所需的最少编辑次数，使得编辑后的$\sigma$与$\pi$之间的Fréchet距离不超过$\delta$。对于编辑操作，我们考虑了三种情况，即顶点删除、顶点插入以及两者兼有。针对这一基本问题，我们探讨了若干变体。具体而言，我们针对离散和连续Fréchet编辑距离变体提出了多项式时间算法，同时给出了弱Fréchet编辑距离变体的难解性结果。