Edit distance is a measure of similarity of two strings based on the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. The edit distance can be computed exactly using a dynamic programming algorithm that runs in quadratic time. Andoni, Krauthgamer, and Onak (2010) gave a nearly linear time algorithm that approximates edit distance within approximation factor poly(log n ). In this article, we provide an algorithm with running time Õ( n 2−2/7 ) that approximates the edit distance within a constant factor.

中文翻译：

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在真正的次二次时间内逼近恒定因子内的编辑距离

编辑距离是基于将一个字符串转换为另一个字符串所需的最小字符插入、删除和替换次数来衡量两个字符串的相似性。可以使用以二次时间运行的动态规划算法精确计算编辑距离。Andoni、Krauthgamer 和 Onak (2010) 给出了一个近似线性的时间算法，该算法在近似因子 poly(logn）。在本文中，我们提供了一个运行时间为 Õ(n 2−2/7) 在一个常数因子内近似编辑距离。