Abstract: We show how to compute the edit distance between two strings of length n up to a factor of 2Õ(sqrt(log n)) in n1+o(1) time. This is the first sub-polynomial approximation algorithm for this problem that runs in near-linear time, improving on the state-of-the-art n1/3+o(1) approximation. Previously, approximation of 2Õ(sqrt(log n)) was known only for embedding edit distance into l1, and it is not known if that embedding can be computed in less than quadratic time.
Comment: Our new paper Polylogarithmic Approximation for Edit Distance and the Asymmetric Query Complexity gives a polylogarithmic approximation algorithm that runs in strongly subquadratic time.