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

CS@BIU

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

10 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

Funding Information:
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).

Publisher Copyright:
© Tsvi Kopelowitz and Ely Porat.

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 [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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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",

author = "Tsvi Kopelowitz and Ely Porat",

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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

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Bibliographical note

Keywords

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