Approximating edit distance in near-linear time

We show how to compute the edit distance between two strings of length n up to a factor of 2 ~O( 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 2 ~O( log n) was known only for embedding edit distance into 1, and it is not known if that embedding can be computed in less than quadratic time. Key words. approximation algorithms, edit distance, metric embeddings AMS subject classifications. 68Q25, 68R15, 68W20, 68W25, 68W40

• Type: Conference
• Year: 2009
• Where: STOC
• Authors: Alexandr Andoni, Krzysztof Onak
• Keywords: Algorithms, Approximation Algorithms, Edit Distance, STOC 2009, Sub-polynomial Approximation Algorithm