research-article

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

Authors:

Arturs Backurs,

Piotr IndykAuthors Info & Claims

STOC '15: Proceedings of the forty-seventh annual ACM symposium on Theory of Computing

Pages 51 - 58

https://doi.org/10.1145/2746539.2746612

Published: 14 June 2015 Publication History

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Abstract

The edit distance (a.k.a. the Levenshtein distance) between two strings is defined as the minimum number of insertions, deletions or substitutions of symbols needed to transform one string into another. The problem of computing the edit distance between two strings is a classical computational task, with a well-known algorithm based on dynamic programming. Unfortunately, all known algorithms for this problem run in nearly quadratic time.

In this paper we provide evidence that the near-quadratic running time bounds known for the problem of computing edit distance might be {tight}. Specifically, we show that, if the edit distance can be computed in time O(n^2-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 M^O(1) 2^(1-ε)N for a constant ε>0. The latter result would violate the Strong Exponential Time Hypothesis, which postulates that such algorithms do not exist.

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Rajput JChandra GJain C(2024)Co-linear chaining on pangenome graphsAlgorithms for Molecular Biology10.1186/s13015-024-00250-w19:1Online publication date: 27-Jan-2024
https://doi.org/10.1186/s13015-024-00250-w
Wang Y(2024)Algorithms for the Uniqueness of the Longest Common SubsequenceJournal of Bioinformatics and Computational Biology10.1142/S021972002350027021:06Online publication date: 10-Jan-2024
https://doi.org/10.1142/S0219720023500270
Williams R(2024)The Orthogonal Vectors Conjecture and Non-Uniform Circuit Lower Bounds2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00088(1372-1387)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00088
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Index Terms

Edit Distance Cannot Be Computed in Strongly Subquadratic Time (unless SETH is false)
1. Theory of computation
  1. Design and analysis of algorithms
    1. Data structures design and analysis
      1. Pattern matching

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Edit Distance Cannot Be Computed in Strongly Subquadratic Time (Unless SETH is False)

The edit distance (a.k.a. the Levenshtein distance) between two strings is defined as the minimum number of insertions, deletions, or substitutions of symbols needed to transform one string into another. The problem of computing the edit distance ...

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Published In

STOC '15: Proceedings of the forty-seventh annual ACM symposium on Theory of Computing

June 2015

916 pages

ISBN:9781450335362

DOI:10.1145/2746539

General Chair:
Rocco Servedio
Columbia University
,
Program Chair:
Ronitt Rubinfeld
MIT and Tel Aviv University

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Association for Computing Machinery

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Publication History

Published: 14 June 2015

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STOC '15

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SIGACT

STOC '15: Symposium on Theory of Computing

June 14 - 17, 2015

Oregon, Portland, USA

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STOC '15 Paper Acceptance Rate 93 of 347 submissions, 27%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

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Rajput JChandra GJain C(2024)Co-linear chaining on pangenome graphsAlgorithms for Molecular Biology10.1186/s13015-024-00250-w19:1Online publication date: 27-Jan-2024
https://doi.org/10.1186/s13015-024-00250-w
Wang Y(2024)Algorithms for the Uniqueness of the Longest Common SubsequenceJournal of Bioinformatics and Computational Biology10.1142/S021972002350027021:06Online publication date: 10-Jan-2024
https://doi.org/10.1142/S0219720023500270
Williams R(2024)The Orthogonal Vectors Conjecture and Non-Uniform Circuit Lower Bounds2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00088(1372-1387)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00088
Chandra GGibney DJain C(2024)Haplotype-aware sequence alignment to pangenome graphsGenome Research10.1101/gr.279143.12434:9(1265-1275)Online publication date: 16-Jul-2024
https://doi.org/10.1101/gr.279143.124
Afshani PKillmann RLarsen K(2024)Hierarchical Categories in Colored SearchingComputational Geometry10.1016/j.comgeo.2024.102090(102090)Online publication date: Mar-2024
https://doi.org/10.1016/j.comgeo.2024.102090
Islam APramanik S(2024)Fast Edit Distance Prediction for All Pairs of Sequences in Very Large NGS DatasetsAdvances in Knowledge Discovery and Data Mining10.1007/978-981-97-2238-9_6(72-91)Online publication date: 1-May-2024
https://doi.org/10.1007/978-981-97-2238-9_6
Boneh IGolan SLevy APorat EShalom B(2024)Burst Edit DistanceString Processing and Information Retrieval10.1007/978-3-031-72200-4_4(41-56)Online publication date: 19-Sep-2024
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Alman JLiang JSong ZZhang RZhuo DOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Bypass exponential time preprocessingProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3668209(48110-48137)Online publication date: 10-Dec-2023
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Cairo MRizzi RTomescu AZirondelli E(2023)Genome Assembly, from Practice to Theory: Safe, Complete and Linear-TimeACM Transactions on Algorithms10.1145/363217620:1(1-26)Online publication date: 8-Nov-2023
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Equi MMäkinen VTomescu AGrossi R(2023)On the Complexity of String Matching for GraphsACM Transactions on Algorithms10.1145/358833419:3(1-25)Online publication date: 12-Apr-2023
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Simulating branching programs with edit distance and friends: or: a polylog shaved is a lower bound made

Approximating Edit Distance in Truly Subquadratic Time: Quantum and MapReduce