Approximating Edit Distance in Near-Linear Time
Data Structures and Algorithms
2011-09-27 v1
Abstract
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.
Cite
@article{arxiv.1109.5635,
title = {Approximating Edit Distance in Near-Linear Time},
author = {Alexandr Andoni and Krzysztof Onak},
journal= {arXiv preprint arXiv:1109.5635},
year = {2011}
}
Comments
Preliminary version appeared in STOC 2009