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 an approximation factor $\text{poly}(\log n)$. In this paper, we provide an algorithm with running time $\tilde{O}(n^{2-2/7})$ that approximates the edit distance within a constant factor.

翻译：编辑距离是根据字符插入、删除和替换的最低数量来测量两个字符串的相似性。 编辑距离可以精确地使用在二次时间运行的动态编程算法来计算。 Andoni, Krauthgamer, 和 Onak (2010年) 给出了近似线性时间算法, 在近似系数 $\ text{poly}(\log n) $( log n) 范围内大约编辑距离。 在本文中, 我们提供了一个运行时间 $\ tilde{ O}( n\\\\ 2-2/7}) 的算法, 接近一个常数内的编辑距离 。