We show that the edit distance between two run-length encoded strings of compressed lengths m and n respectively, can be computed in O(mnlog(mn)) time. This improves the previous record by a factor of 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.
@article{arxiv.1905.01254,
title = {RLE edit distance in near optimal time},
author = {Raphaël Clifford and Paweł Gawrychowski and Tomasz Kociumaka and Daniel P. Martin and Przemysław Uznański},
journal= {arXiv preprint arXiv:1905.01254},
year = {2019}
}