Fréchet Edit Distance

Abstract

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.