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arXiv · 1905.01254

RLE edit distance in near optimal time

Raphaël Clifford·Paweł Gawrychowski·Tomasz Kociumaka·Daniel P. Martin·Przemysław Uznański
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Abstract

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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Raphaël Clifford, Paweł Gawrychowski, Tomasz Kociumaka, Daniel P. Martin, Przemysław Uznański. 2019-05-03. RLE edit distance in near optimal time. https://arxiv.org/abs/1905.01254

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