The paper presents a discrete variation of the Fréchet distance between closed curves, which can be seen as an approximation of the continuous measure. A rather straightforward approach to compute the discrete Fréchet distance between two closed sequences of m and n points using binary search takes $\mathcal{O}(mn\log mn)$ time. We present an algorithm that takes $\mathcal{O}(mn{\log }^{⁎}mn)$ time, where ${\log }^{⁎}$ is the iterated logarithm.

中文翻译：

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闭合曲线的离散 Fréchet 距离

该论文提出了闭合曲线之间 Fréchet 距离的离散变化，可以将其视为连续测度的近似值。使用二进制搜索计算两个m和n点闭合序列之间的离散 Fréchet 距离的一种相当直接的方法需要$\mathcal{欧}(米n\mathrm{日志}米n)$时间。我们提出了一种算法$\mathcal{欧}(米n{\mathrm{日志}}^{⁎}米n)$时间，地点${\mathrm{日志}}^{⁎}$是迭代对数。