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Edit distance is a measure of similarity of two strings based on the minimumnumber of character insertions, deletions, and substitutions required totransform one string into the other. The edit distance can be computed exactlyusing a dynamic programming algorithm that runs in quadratic time. Andoni,Krauthgamer, and Onak (2010) gave a nearly linear time algorithm thatapproximates edit distance within an approximation factor $\text{poly}(\logn)$.  In this paper, we provide an algorithm with running time$\tilde{O}(n^{2-2/7})$ that approximates the edit distance within a constantfactor.

Approximating Edit Distance Within Constant Factor in Truly Sub-Quadratic Time