@article{Clifford2019RLEED,
title={RLE edit distance in near optimal time},
author={R. Clifford and Pawel Gawrychowski and Tomasz Kociumaka and D. Martin and P. Uznanski},
journal={ArXiv},
year={2019},
volume={abs/1905.01254}
}

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.