Faster algorithms for string matching with k mismatches

Amihood Amir; Moshe Lewenstein; Ely Porat

doi:10.1016/S0196-6774(03)00097-X

Faster algorithms for string matching with k mismatches

Amihood Amir
, Moshe Lewenstein
, Ely Porat

Department of Computer Science

Georgia Institute of Technology

Research output: Contribution to journal › Article › peer-review

144 Scopus citations

Abstract

The string matching with mismatches problem is that of finding the number of mismatches between a pattern P of length m and every length m substring of the text T. Currently, the fastest algorithms for this problem are the following. The Galil-Giancarlo algorithm finds all locations where the pattern has at most k errors (where k is part of the input) in time O(nk). The Abrahamson algorithm finds the number of mismatches at every location in time O(n√m log m). We present an algorithm that is faster than both. Our algorithm finds all locations where the pattern has at most k errors in time O(n√k log k). We also show an algorithm that solves the above problem in time O((n + (nk³)/m) log k).

Original language	English
Pages (from-to)	257-275
Number of pages	19
Journal	Journal of Algorithms
Volume	50
Issue number	2
DOIs	https://doi.org/10.1016/S0196-6774(03)00097-X
State	Published - Feb 2004

Bibliographical note

Funding Information:
* Corresponding author. E-mail addresses: [email protected] (A. Amir), [email protected] (M. Lewenstein), [email protected] (E. Porat). 1 Partially supported by NSF grant CCR-96-10170, BSF grant 96-00509, and a BIU internal research grant.

Funding

* Corresponding author. E-mail addresses: [email protected] (A. Amir), [email protected] (M. Lewenstein), [email protected] (E. Porat). 1 Partially supported by NSF grant CCR-96-10170, BSF grant 96-00509, and a BIU internal research grant.

Funders	Funder number
National Science Foundation	CCR-96-10170
United States-Israel Binational Science Foundation	96-00509

Keywords

Approximate string matching
Combinatorial algorithms on words
Design and analysis of algorithms
Hamming distance

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10.1016/S0196-6774(03)00097-X

Cite this

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title = "Faster algorithms for string matching with k mismatches",

abstract = "The string matching with mismatches problem is that of finding the number of mismatches between a pattern P of length m and every length m substring of the text T. Currently, the fastest algorithms for this problem are the following. The Galil-Giancarlo algorithm finds all locations where the pattern has at most k errors (where k is part of the input) in time O(nk). The Abrahamson algorithm finds the number of mismatches at every location in time O(n√m log m). We present an algorithm that is faster than both. Our algorithm finds all locations where the pattern has at most k errors in time O(n√k log k). We also show an algorithm that solves the above problem in time O((n + (nk3)/m) log k).",

keywords = "Approximate string matching, Combinatorial algorithms on words, Design and analysis of algorithms, Hamming distance",

author = "Amihood Amir and Moshe Lewenstein and Ely Porat",

note = "Funding Information: * Corresponding author. E-mail addresses: [email protected] (A. Amir), [email protected] (M. Lewenstein), [email protected] (E. Porat). 1 Partially supported by NSF grant CCR-96-10170, BSF grant 96-00509, and a BIU internal research grant.",

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AU - Lewenstein, Moshe

AU - Porat, Ely

N1 - Funding Information: * Corresponding author. E-mail addresses: [email protected] (A. Amir), [email protected] (M. Lewenstein), [email protected] (E. Porat). 1 Partially supported by NSF grant CCR-96-10170, BSF grant 96-00509, and a BIU internal research grant.

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N2 - The string matching with mismatches problem is that of finding the number of mismatches between a pattern P of length m and every length m substring of the text T. Currently, the fastest algorithms for this problem are the following. The Galil-Giancarlo algorithm finds all locations where the pattern has at most k errors (where k is part of the input) in time O(nk). The Abrahamson algorithm finds the number of mismatches at every location in time O(n√m log m). We present an algorithm that is faster than both. Our algorithm finds all locations where the pattern has at most k errors in time O(n√k log k). We also show an algorithm that solves the above problem in time O((n + (nk3)/m) log k).

AB - The string matching with mismatches problem is that of finding the number of mismatches between a pattern P of length m and every length m substring of the text T. Currently, the fastest algorithms for this problem are the following. The Galil-Giancarlo algorithm finds all locations where the pattern has at most k errors (where k is part of the input) in time O(nk). The Abrahamson algorithm finds the number of mismatches at every location in time O(n√m log m). We present an algorithm that is faster than both. Our algorithm finds all locations where the pattern has at most k errors in time O(n√k log k). We also show an algorithm that solves the above problem in time O((n + (nk3)/m) log k).

KW - Approximate string matching

KW - Combinatorial algorithms on words

KW - Design and analysis of algorithms

KW - Hamming distance

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ER -

Faster algorithms for string matching with k mismatches

Abstract

Bibliographical note

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Keywords

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