  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.
