We define and study the Fréchet distance and the discrete Fréchet distance between two point sets in the plane. One problem based on the well-known Fréchet distance is to find a polygonal curve on a point set with small Fréchet distance or small discrete Fréchet distance to another given polygonal curve. Here, we consider two given point sets and ask if permutations of these point sets exist, such that the Fréchet distance or the discrete Fréchet distance of curves defined by the permutations is small.

中文翻译：

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两个点集之间的 Fréchet 距离

我们定义和研究平面中两个点集之间的 Fréchet 距离和离散 Fréchet 距离。基于众所周知的 Fréchet 距离的一个问题是在一个点集上找到一条多边形曲线，该点集与另一条给定的多边形曲线具有小的 Fréchet 距离或小的离散 Fréchet 距离。在这里，我们考虑两个给定的点集，并询问这些点集的排列是否存在，使得由排列定义的曲线的 Fréchet 距离或离散 Fréchet 距离很小。