Pattern matching with swaps

Amihood Amir; Yonatan Aumann; Gad M. Landau; Moshe Lewenstein; Noa Lewenstein

Pattern matching with swaps

Amihood Amir
, Yonatan Aumann
, Gad M. Landau
, Moshe Lewenstein
, Noa Lewenstein

Bar-Ilan University

Research output: Contribution to journal › Conference article › peer-review

27 Scopus citations

Abstract

Let a text string T of n symbols and a pattern string P of m symbols from alphabet Σ be given. A swapped version T′ of T is a length n string derived from T by a series of local swaps, (i.e. t′_l←t_l+1 and t′_l+1←t_l) where each element can participate in no more than one swap. The Pattern Matching with Swaps problem is that of finding all locations i for which there exists a swapped version T′ of T where there is an exact matching of P in location i of T′. It has been an open problem whether swapped matching can be done in less than O(mn) time. In this paper we show the first algorithm that solves the pattern matching with swaps problem in time o(mn). We present an algorithm whose time complexity is O(nm^1/3 log m log² σ) for a general alphabet Σ, where σ = min(m, |Σ|).

Original language	English
Pages (from-to)	144-153
Number of pages	10
Journal	Annual Symposium on Foundations of Computer Science - Proceedings
State	Published - 1997
Event	Proceedings of the 1997 38th IEEE Annual Symposium on Foundations of Computer Science - Miami Beach, FL, USA Duration: 20 Oct 1997 → 22 Oct 1997

Bibliographical note

Funding Information:
1A preliminary version of this paper appeared in FOCS 97. 2Partially supported by NSF grant CCR-96-10170, BSF grant 96-00509, and a BIU internal research grant. 3Partially supported by NSF grants CCR-9305873 and CCR-9610238 and by the Israel Science Foundation founded by the Israeli Academy of Sciences and Humanities. 4Partially supported by the Israel Ministry of Science and Arts Grant 8560.

Funding

1A preliminary version of this paper appeared in FOCS 97. 2Partially supported by NSF grant CCR-96-10170, BSF grant 96-00509, and a BIU internal research grant. 3Partially supported by NSF grants CCR-9305873 and CCR-9610238 and by the Israel Science Foundation founded by the Israeli Academy of Sciences and Humanities. 4Partially supported by the Israel Ministry of Science and Arts Grant 8560.

Funders	Funder number
Israel Ministry of Science and Arts	8560
Israeli Academy of Sciences and Humanities
National Science Foundation	CCR-96-10170
Bloom's Syndrome Foundation	CCR-9305873, CCR-9610238, 96-00509
Israel Science Foundation

Cite this

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title = "Pattern matching with swaps",

abstract = "Let a text string T of n symbols and a pattern string P of m symbols from alphabet Σ be given. A swapped version T′ of T is a length n string derived from T by a series of local swaps, (i.e. t′l←tl+1 and t′l+1←tl) where each element can participate in no more than one swap. The Pattern Matching with Swaps problem is that of finding all locations i for which there exists a swapped version T′ of T where there is an exact matching of P in location i of T′. It has been an open problem whether swapped matching can be done in less than O(mn) time. In this paper we show the first algorithm that solves the pattern matching with swaps problem in time o(mn). We present an algorithm whose time complexity is O(nm1/3 log m log2 σ) for a general alphabet Σ, where σ = min(m, |Σ|).",

author = "Amihood Amir and Yonatan Aumann and Landau, \{Gad M.\} and Moshe Lewenstein and Noa Lewenstein",

note = "Funding Information: 1A preliminary version of this paper appeared in FOCS 97. 2Partially supported by NSF grant CCR-96-10170, BSF grant 96-00509, and a BIU internal research grant. 3Partially supported by NSF grants CCR-9305873 and CCR-9610238 and by the Israel Science Foundation founded by the Israeli Academy of Sciences and Humanities. 4Partially supported by the Israel Ministry of Science and Arts Grant 8560.; Proceedings of the 1997 38th IEEE Annual Symposium on Foundations of Computer Science ; Conference date: 20-10-1997 Through 22-10-1997",

year = "1997",

language = "אנגלית",

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journal = "Annual Symposium on Foundations of Computer Science - Proceedings",

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AU - Amir, Amihood

AU - Aumann, Yonatan

AU - Landau, Gad M.

AU - Lewenstein, Moshe

AU - Lewenstein, Noa

N1 - Funding Information: 1A preliminary version of this paper appeared in FOCS 97. 2Partially supported by NSF grant CCR-96-10170, BSF grant 96-00509, and a BIU internal research grant. 3Partially supported by NSF grants CCR-9305873 and CCR-9610238 and by the Israel Science Foundation founded by the Israeli Academy of Sciences and Humanities. 4Partially supported by the Israel Ministry of Science and Arts Grant 8560.

PY - 1997

Y1 - 1997

N2 - Let a text string T of n symbols and a pattern string P of m symbols from alphabet Σ be given. A swapped version T′ of T is a length n string derived from T by a series of local swaps, (i.e. t′l←tl+1 and t′l+1←tl) where each element can participate in no more than one swap. The Pattern Matching with Swaps problem is that of finding all locations i for which there exists a swapped version T′ of T where there is an exact matching of P in location i of T′. It has been an open problem whether swapped matching can be done in less than O(mn) time. In this paper we show the first algorithm that solves the pattern matching with swaps problem in time o(mn). We present an algorithm whose time complexity is O(nm1/3 log m log2 σ) for a general alphabet Σ, where σ = min(m, |Σ|).

AB - Let a text string T of n symbols and a pattern string P of m symbols from alphabet Σ be given. A swapped version T′ of T is a length n string derived from T by a series of local swaps, (i.e. t′l←tl+1 and t′l+1←tl) where each element can participate in no more than one swap. The Pattern Matching with Swaps problem is that of finding all locations i for which there exists a swapped version T′ of T where there is an exact matching of P in location i of T′. It has been an open problem whether swapped matching can be done in less than O(mn) time. In this paper we show the first algorithm that solves the pattern matching with swaps problem in time o(mn). We present an algorithm whose time complexity is O(nm1/3 log m log2 σ) for a general alphabet Σ, where σ = min(m, |Σ|).

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JF - Annual Symposium on Foundations of Computer Science - Proceedings

T2 - Proceedings of the 1997 38th IEEE Annual Symposium on Foundations of Computer Science

Y2 - 20 October 1997 through 22 October 1997

ER -

Pattern matching with swaps

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Bibliographical note

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