# RLE edit distance in near optimal time

## TL;DR

This paper presents a near-optimal algorithm for computing edit distance between run-length encoded strings, significantly improving previous results and approaching theoretical limits under standard complexity assumptions.

## Contribution

The authors develop an algorithm that computes run-length encoded edit distance in near-optimal time, closing a research gap since 1993.

## Key findings

- Achieves $ ilde{O}(mn)$ time complexity for run-length encoded strings.
- Improves previous algorithms by a factor of $ ilde{n}/ ext{log}(mn)$.
- Time complexity is near optimal under SETH-hardness.

## Abstract

We show that the edit distance between two run-length encoded strings of compressed lengths $m$ and $n$ respectively, can be computed in $\mathcal{O}(mn\log(mn))$ time. This improves the previous record by a factor of $\mathcal{O}(n/\log(mn))$. The running time of our algorithm is within subpolynomial factors of being optimal, subject to the standard SETH-hardness assumption. This effectively closes a line of algorithmic research first started in 1993.