# 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} }

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…

## 8 Citations

A Simple Sublinear Algorithm for Gap Edit Distance

- Mathematics, Computer ScienceArXiv
- 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.

Locality-Preserving Hashing for Shifts with Connections to Cryptography

- Computer Science
- 2022

Can we sense our location in an unfamiliar environment by taking a sublinear-size sample of our surroundings? Can we efficiently encrypt a message that only someone physically close to us can…

An Improved Sketching Algorithm for Edit Distance

- Computer ScienceSTACS
- 2021

Improved upper bounds for the simultaneous sketching complexity of edit distance are provided and an improved analysis demonstrating that a slight modification of their construction achieves a bound of Õ(k3).

Approximation Algorithms for Large Scale Data Analysis

- Computer SciencePODS
- 2021

New facets of fast algorithm design for large scale data analysis that emphasizes on the role of developing approximation algorithms for better polynomial time/query complexity are covered.

Gap Edit Distance via Non-Adaptive Queries: Simple and Optimal

- Computer ScienceArXiv
- 2021

This work designs a non-adaptive algorithm with query complexity Õ( n kc−0.5 ), and proves that this bound is optimal up to polylogarithmic factors, and achieves optimal time complexity â‚¬1.5.

An Improved Sketching Bound for Edit Distance

- Computer Science, MathematicsArXiv
- 2020

Improved upper bounds for the simultaneous sketching complexity of edit distance are provided and an improved analysis is provided demonstrating that a slight modification of their construction achieves a bound of $\tilde O(k^3)$.

Simple Constant-Factor Approximation to Edit Distance

- 2020

We show a simple algorithm for estimating edit distance between two strings in strongly subquadratic time, up to 3+ approximation. The recent couple years have seen a “new generation” of edit…

Table of Contents

- JAAD Case Reports
- 2020

Lifting with Simple Gadgets and Applications to Circuit and Proof Complexity 24 Susanna de Rezende (Institute of Mathematics of the Czech Academy of Sciences, Czech Republic), Or Meir (University of…

## References

SHOWING 1-10 OF 57 REFERENCES

A Simple Sublinear Algorithm for Gap Edit Distance

- Mathematics, Computer ScienceArXiv
- 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.

Polylogarithmic Approximation for Edit Distance and the Asymmetric Query Complexity

- Mathematics, Computer Science2010 IEEE 51st Annual Symposium on Foundations of Computer Science
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The lower bound is the first to expose hardness of edit distance stemming from the input strings being ``repetitive'', which means that many of their substrings are approximately identical, and provides the first rigorous separation between edit distance and Ulam distance.

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.

On Estimating Edit Distance: Alignment, Dimension Reduction, and Embeddings

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It is shown that any algorithm to estimate edit distance can be used in a black-box fashion to produce an approximate alignment of strings, with modest loss in approximation factor and small loss in run time.

Approximating edit distance in near-linear time

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This is the first sub-polynomial approximation algorithm for this problem that runs in near-linear time, improving on the state-of-the-art n<sup>(1/3+o(1)) approximation.

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- Mathematics, Computer Science45th Annual IEEE Symposium on Foundations of Computer Science
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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.

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).

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

- Mathematics, Computer Science2020 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.

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This work considers the problem of constructing binary codes to recover from bit deletions with efficient encoding/decoding, and constructs a binary code with redundancy that can be decoded from <inline-formula> <tex-math notation="LaTeX">$k$ </tex-Math></inline- formula>-fold repetition code.

Edit Distance Cannot Be Computed in Strongly Subquadratic Time (unless SETH is false)

- Computer Science, MathematicsSTOC
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This paper shows that, if the edit distance can be computed in time O(n2-δ) for some constant δ>0, then the satisfiability of conjunctive normal form formulas with N variables and M clauses can be solved in time MO(1) 2(1-ε)N for a constant ε>0.