# Approximating Edit Distance within Constant Factor in Truly Sub-Quadratic Time

@article{Chakraborty2018ApproximatingED, title={Approximating Edit Distance within Constant Factor in Truly Sub-Quadratic Time}, author={Diptarka Chakraborty and Debarati Das and Elazar Goldenberg and Michal Kouck{\'y} and Michael E. Saks}, journal={2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)}, year={2018}, pages={979-990} }

Edit distance is a measure of similarity of two strings based on the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. The edit distance can be computed exactly using a dynamic programming algorithm that runs in quadratic time. Andoni, Krauthgamer and Onak (2010) gave a nearly linear time algorithm that approximates edit distance within approximation factor poly(log n). In this paper, we provide an algorithm with running time…

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## 75 Citations

Simple Constant-Factor Approximation to Edit Distance

- Computer Science
- 2020

A simple algorithm for estimating edit distance between two strings in strongly subquadratic time, up to 3+ approximation, and matches the runtime of the fastest such algorithm for 3 + approximation from the independent work of [GRS20].

Edit Distance in Near-Linear Time: it's a Constant Factor

- Computer Science, Mathematics2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
- 2020

The result completes a research direction set forth in the recent breakthrough paper, which showed the first constant-factor approximation algorithm with a (strongly) sub-quadratic running time.

Sublinear Algorithms for Gap Edit Distance

- Computer Science, Mathematics2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
- 2019

An algorithm for distinguishing whether the edit distance is at most t or at least t^2 (the quadratic gap problem) in time Õ(n/t+t^3).

3+ε Approximation of Tree Edit Distance in Truly Subquadratic Time

- Computer Science, MathematicsITCS
- 2022

This work gives a truly subquadratic time algorithm that approximates tree edit distance within a factor 3 + ε.

Constant-factor approximation of near-linear edit distance in near-linear time

- Mathematics, Computer ScienceSTOC
- 2020

We show that the edit distance between two strings of length n can be computed via a randomized algorithm within a factor of f(є) in n 1+є time as long as the edit distance is at least n 1−δ for some…

Reducing approximate Longest Common Subsequence to approximate Edit Distance

- Computer ScienceSODA
- 2020

This work gives a reduction from approximate LCS to approximate Edit Distance, yielding the first efficient $(1/2+\epsilon)$-approximation algorithm for LCS for some constant $\epssilon>0$.

C C ] 2 O ct 2 01 9 Sublinear Algorithms for Gap Edit Distance ∗

- Computer Science
- 2019

An algorithm for distinguishing whether the edit distance is at most t or at least t2 (the quadratic gap problem) in time Õ( t + t 3) that is sublinear roughly for all t in [ω(1), o(n1/3)], which was not known before.

Simpler Constant-Factor Approximation to Edit Distance Problems

- Computer Science
- 2018

An alternative implementation of the core idea from [DGKS18] is provided, with the main goal of developing a simpler constant-factor approximation algorithm with sub-quadratic run-time, while achieving the best possible bounds.

Constant factor approximations to edit distance on far input pairs in nearly linear time

- Mathematics, Computer ScienceSTOC
- 2020

On any input with edit(x,y) ≥ n 1−ζ the algorithm outputs a constant factor approximation with high probability and this result has been proven independently by Brakensiek and Rubinstein.

A Simple Sublinear Algorithm for Gap Edit Distance

- Computer Science, MathematicsArXiv
- 2020

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.

## References

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Edit Distance in Near-Linear Time: it's a Constant Factor

- Computer Science, Mathematics2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
- 2020

The result completes a research direction set forth in the recent breakthrough paper, which showed the first constant-factor approximation algorithm with a (strongly) sub-quadratic running time.

Approximating Edit Distance in Truly Subquadratic Time: Quantum and MapReduce

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This work provides a quantum constant approximation algorithm for computing the edit distance in truly subquadratic time, and provides a MapReduce algorithm to approximate edit distance within a factor of $3, with sublinearly many machines and sublinear memory.

Constant-factor approximation of near-linear edit distance in near-linear time

- Mathematics, Computer ScienceSTOC
- 2020

We show that the edit distance between two strings of length n can be computed via a randomized algorithm within a factor of f(є) in n 1+є time as long as the edit distance is at least n 1−δ for some…

Simpler Constant-Factor Approximation to Edit Distance Problems

- Computer Science
- 2018

An alternative implementation of the core idea from [DGKS18] is provided, with the main goal of developing a simpler constant-factor approximation algorithm with sub-quadratic run-time, while achieving the best possible bounds.

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Constant factor approximations to edit distance on far input pairs in nearly linear time

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On any input with edit(x,y) ≥ n 1−ζ the algorithm outputs a constant factor approximation with high probability and this result has been proven independently by Brakensiek and Rubinstein.

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Algorithms are developed that solve gap versions of the edit distance problem: given two strings of length n with the promise that their edit distance is either at most k or greater than /spl lscr/, decide which of the two holds and develop an n/sup 3/7/-approximation quasilinear time algorithm.

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This paper presents two streaming algorithms for computing edit distance, one which runs in time $O(n+k^2)$ and the other which is known to be optimal under the Strong Exponential Time Hypothesis.

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