Approximating Edit Distance in Near-Linear Time
Alexandr Andoni, Krzysztof Onak · SIAM Journal on Computing · 2012
We show how to compute the edit distance between two strings of length $n$ up to a factor of $2^{\tilde{O}(\sqrt{\log n})}$ in $n^{1+o(1)}$ time. This is the first subpolynomial approximation algorithm for this problem that runs in near-linear time, improving on the state-of-the-art $n^{1/3+o(1)}$ approximation. Previously, approximation of $2^{\tilde{O}(\sqrt{\log n})}$ was known only for embedding edit distance into $\ell_1$, and it is not known if that embedding can be computed in less than quadratic time.