Approximating Edit Distance in Near-Linear Time

TL;DR

This paper presents a near-linear time algorithm that approximates the edit distance between two strings within a factor of 2^{~O(sqrt(log n))}, significantly improving the efficiency over previous methods.

Contribution

It introduces the first sub-polynomial approximation algorithm for edit distance that operates in near-linear time, surpassing prior cubic-root approximation approaches.

Findings

Achieves approximation within a factor of 2^{~O(sqrt(log n))}

Runs in n^{1+o(1)} time, nearly linear

Improves upon previous n^{1/3+o(1)} approximation algorithms

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.