  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.
