AI 中文总结
针对c-填充曲线间弗雷歇距离的众多变体，提出线性时间(1+ε)-近似算法，核心是高程函数线性大小近似及隐式动态规划，运行时间约O(cn/ε)，去除先前算法对数因子，算法简单且适用其他输入。
AI 中文摘要
我们为c-填充曲线（其中c∈O(1)）之间的弗雷歇距离的众多变体给出了线性时间且最优的(1+ε)-近似算法，去除了先前算法中存在的额外对数因子。新算法的关键是高程函数的线性大小近似，它使用将域分解为矩形，并在此分解上进行仔细的隐式动态规划。该算法扩展到强、弱、离散和连续弗雷歇距离，运行时间约为O(cn/ε)。c-填充假设仅用于分析，算法简单且对其他输入也应有效。
英文摘要
We give linear-time, and thus optimal, $(1+\varepsilon)$-approximation algorithms for numerous variants of the Frechet distance between $c$-packed curves (where $c \in O(1)$), removing an additional log factor that was present in previous algorithms. The key to our new algorithms is a linear-size approximation of the elevation function, which uses a decomposition of the domain into rectangles, and a careful implicit dynamic programming on this decomposition. The algorithm extends to the strong, weak, discrete, and continuous Frechet distances with a running time of roughly $O(cn/\varepsilon)$. The $c$-packedness assumption is used only in the analysis, and the algorithm is simple and should work efficiently for other inputs.
