Approximating Edit Distance Within Constant Factor in Truly Sub-Quadratic Time

TL;DR

This paper presents a new algorithm that approximates the edit distance between two strings within a constant factor in truly sub-quadratic time, significantly improving efficiency over previous methods.

Contribution

The authors develop a novel algorithm achieving constant factor approximation of edit distance in ilde{O}(n^{2-2/7}) time, surpassing prior nearly linear time approximations.

Findings

Achieves constant factor approximation in sub-quadratic time

Runs in ilde{O}(n^{2-2/7}) time, faster than quadratic

Improves efficiency of approximate edit distance computation

Abstract

Edit distance is a measure of similarity of two strings based on the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. The edit distance can be computed exactly using a dynamic programming algorithm that runs in quadratic time. Andoni, Krauthgamer, and Onak (2010) gave a nearly linear time algorithm that approximates edit distance within an approximation factor $\text{poly}(\log n)$. In this paper, we provide an algorithm with running time $\tilde{O}(n^{2-2/7})$ that approximates the edit distance within a constant factor.