Approximating Edit Distance in Near-Linear Time

Computer Science – Data Structures and Algorithms

Scientific paper

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Preliminary version appeared in STOC 2009

Scientific paper

We show how to compute the edit distance between two strings of length n up to a factor of 2^{\~O(sqrt(log n))} in n^(1+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 n^(1/3+o(1)) approximation. Previously, approximation of 2^{\~O(sqrt(log n))} was known only for embedding edit distance into l_1, and it is not known if that embedding can be computed in less than quadratic time.

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