RLE edit distance in near optimal time.

We show that the edit distance between two run-length encoded strings of compressed lengths $m$ and $n$ respectively, can be computed in $mathcal{O}(mnlog(mn))$ 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.