A simple algorithm for approximating the text-to-pattern hamming distance

Tsvi Kopelowitz; Ely Porat

doi:10.4230/OASIcs.SOSA.2018.10

A simple algorithm for approximating the text-to-pattern hamming distance

Tsvi Kopelowitz, Ely Porat

Department of Computer Science

University of Waterloo

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

13 Scopus citations

Abstract

The algorithmic task of computing the Hamming distance between a given pattern of length m and each location in a text of length n, both over a general alphabet Σ, is one of the most fundamental algorithmic tasks in string algorithms. The fastest known runtime for exact computation is Õ(n √m). We recently introduced a complicated randomized algorithm for obtaining a 1 ± ∈ approximation for each location in the text in O(n/∈ log 1/∈ log n log m log |Σ|) total time, breaking a barrier that stood for 22 years. In this paper, we introduce an elementary and simple randomized algorithm that takes O(n/∈ log n log m) time.

Original language	English
Title of host publication	1st Symposium on Simplicity in Algorithms, SOSA 2018 - Co-located with the 29th ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
Editors	Raimund Seidel
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959770644
DOIs	https://doi.org/10.4230/OASIcs.SOSA.2018.10
State	Published - 1 Jan 2018
Event	1st Symposium on Simplicity in Algorithms, SOSA 2018 - New Orleans, United States Duration: 7 Jan 2018 → 10 Jan 2018

Publication series

Name	OpenAccess Series in Informatics
Volume	61
ISSN (Print)	2190-6807

Conference

Conference	1st Symposium on Simplicity in Algorithms, SOSA 2018
Country/Territory	United States
City	New Orleans
Period	7/01/18 → 10/01/18

Bibliographical note

Publisher Copyright:
© Tsvi Kopelowitz and Ely Porat.

Funding

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 683064).

Funders	Funder number
European Union's Horizon 2020 research and innovation programme
Horizon 2020 Framework Programme	683064
European Commission

Keywords

Approximation algorithms
Hamming distance
Pattern matching

Access to Document

10.4230/OASIcs.SOSA.2018.10

Cite this

Kopelowitz, T., & Porat, E. (2018). A simple algorithm for approximating the text-to-pattern hamming distance. In R. Seidel (Ed.), 1st Symposium on Simplicity in Algorithms, SOSA 2018 - Co-located with the 29th ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 Article 10 (OpenAccess Series in Informatics; Vol. 61). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/OASIcs.SOSA.2018.10

Kopelowitz, Tsvi ; Porat, Ely. / A simple algorithm for approximating the text-to-pattern hamming distance. 1st Symposium on Simplicity in Algorithms, SOSA 2018 - Co-located with the 29th ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. editor / Raimund Seidel. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. (OpenAccess Series in Informatics).

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title = "A simple algorithm for approximating the text-to-pattern hamming distance",

abstract = "The algorithmic task of computing the Hamming distance between a given pattern of length m and each location in a text of length n, both over a general alphabet Σ, is one of the most fundamental algorithmic tasks in string algorithms. The fastest known runtime for exact computation is {\~O}(n √m). We recently introduced a complicated randomized algorithm for obtaining a 1 ± ∈ approximation for each location in the text in O(n/∈ log 1/∈ log n log m log |Σ|) total time, breaking a barrier that stood for 22 years. In this paper, we introduce an elementary and simple randomized algorithm that takes O(n/∈ log n log m) time.",

keywords = "Approximation algorithms, Hamming distance, Pattern matching",

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Kopelowitz, T & Porat, E 2018, A simple algorithm for approximating the text-to-pattern hamming distance. in R Seidel (ed.), 1st Symposium on Simplicity in Algorithms, SOSA 2018 - Co-located with the 29th ACM-SIAM Symposium on Discrete Algorithms, SODA 2018., 10, OpenAccess Series in Informatics, vol. 61, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 1st Symposium on Simplicity in Algorithms, SOSA 2018, New Orleans, United States, 7/01/18. https://doi.org/10.4230/OASIcs.SOSA.2018.10

A simple algorithm for approximating the text-to-pattern hamming distance. / Kopelowitz, Tsvi ; Porat, Ely.
1st Symposium on Simplicity in Algorithms, SOSA 2018 - Co-located with the 29th ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. ed. / Raimund Seidel. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. 10 (OpenAccess Series in Informatics; Vol. 61).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Kopelowitz T , Porat E. A simple algorithm for approximating the text-to-pattern hamming distance. In Seidel R, editor, 1st Symposium on Simplicity in Algorithms, SOSA 2018 - Co-located with the 29th ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2018. 10. (OpenAccess Series in Informatics). doi: 10.4230/OASIcs.SOSA.2018.10

A simple algorithm for approximating the text-to-pattern hamming distance

Abstract

Publication series

Conference

Bibliographical note

Funding

Keywords

Access to Document

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