# Constant-factor approximation of near-linear 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 constant factor, especially effective when the edit distance is relatively large.

## Contribution

It introduces a near-linear time approximation algorithm for edit distance that works efficiently when the distance is above a certain threshold.

## Key findings

- Approximate edit distance within a constant factor in near-linear time
- Effective for strings with large edit distance
- Bridges gap between exact computation and efficiency

## Abstract

We show that the edit distance between two strings of length $n$ can be computed within a factor of $f(\epsilon)$ in $n^{1+\epsilon}$ time as long as the edit distance is at least $n^{1-\delta}$ for some $\delta(\epsilon) > 0$.