RLE edit distance in near optimal time

@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}
}
  • R. Clifford, Pawel Gawrychowski, +2 authors P. Uznanski
  • Published 2019
  • Mathematics, Computer Science
  • ArXiv
  • 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. 
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