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The Cartographer
RLE edit distance in near optimal time
May 03, 2019 Β· Declared Dead Β· π International Symposium on Mathematical Foundations of Computer Science
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Authors
RaphaΓ«l Clifford, PaweΕ Gawrychowski, Tomasz Kociumaka, Daniel P. Martin, PrzemysΕaw UznaΕski
arXiv ID
1905.01254
Category
cs.DS: Data Structures & Algorithms
Citations
8
Venue
International Symposium on Mathematical Foundations of Computer Science
Last Checked
4 months ago
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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