Sublinear-Time Algorithms for Computing & Embedding Gap Edit Distance

@article{Kociumaka2020SublinearTimeAF,
  title={Sublinear-Time Algorithms for Computing \& Embedding Gap Edit Distance},
  author={Tomasz Kociumaka and Barna Saha},
  journal={2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)},
  year={2020},
  pages={1168-1179}
}
  • Tomasz Kociumaka, B. Saha
  • Published 24 July 2020
  • Computer Science, Mathematics
  • 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
In this paper, we design new sublinear-time algorithms for solving the gap edit distance problem and for embedding edit distance to Hamming distance. For the gap edit distance problem, we give a greedy algorithm that distinguishes in time <tex>$\tilde{\mathcal{O}}(\frac{n}{k}+k^{2})$</tex> between length-n input strings with edit distance at most <tex>$k$</tex> and those with edit distance more than <tex>$4k^{2}$</tex>. This is an improvement and a simplification upon the main result of… 
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References

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TLDR
The main result is a very simple algorithm for this benchmark that settles the open problem of obtaining a truly sublinear time for the entire range of relevant $k$ and obtains a $k-vs-$k^2$ algorithm for the one-sided preprocessing model.
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TLDR
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TLDR
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TLDR
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TLDR
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TLDR
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