Charge and reduce: A fixed-parameter algorithm for String-to-String Correction
String distance problems typically ask for a minimum number of permitted operations to transform one string into another. Such problems find application in a wide variety of areas, including error-correcting codes, parsing theory, speech recognition, and computational biology, to name a few. Here we...
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| Veröffentlicht in: | Discrete optimization Jg. 8; H. 1; S. 41 - 49 |
|---|---|
| Hauptverfasser: | , , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Elsevier B.V
01.02.2011
|
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| ISSN: | 1572-5286, 1873-636X |
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| Abstract | String distance problems typically ask for a minimum number of permitted operations to transform one string into another. Such problems find application in a wide variety of areas, including error-correcting codes, parsing theory, speech recognition, and computational biology, to name a few. Here we consider a classic string distance problem, the
N
P
-complete
String-to-String Correction problem, first studied by Wagner some 35 years ago. In this problem, we are asked whether it is possible to transform string
x
into string
y
with at most
k
operations on
x
, where permitted operations are single-character deletions and adjacent character exchanges. We prove that
String-to-String Correction is fixed-parameter tractable, for parameter
k
, and present a simple fixed-parameter algorithm that solves the problem in
O
(
2
k
n
)
time. We also devise a bounded search tree algorithm, and introduce a bookkeeping technique that we call
charge and reduce. This leads to an algorithm whose running time is
O
(
1.618
1
k
n
)
. |
|---|---|
| AbstractList | String distance problems typically ask for a minimum number of permitted operations to transform one string into another. Such problems find application in a wide variety of areas, including error-correcting codes, parsing theory, speech recognition, and computational biology, to name a few. Here we consider a classic string distance problem, the
N
P
-complete
String-to-String Correction problem, first studied by Wagner some 35 years ago. In this problem, we are asked whether it is possible to transform string
x
into string
y
with at most
k
operations on
x
, where permitted operations are single-character deletions and adjacent character exchanges. We prove that
String-to-String Correction is fixed-parameter tractable, for parameter
k
, and present a simple fixed-parameter algorithm that solves the problem in
O
(
2
k
n
)
time. We also devise a bounded search tree algorithm, and introduce a bookkeeping technique that we call
charge and reduce. This leads to an algorithm whose running time is
O
(
1.618
1
k
n
)
. |
| Author | Abu-Khzam, Faisal N. Lee-Cultura, Serena Fernau, Henning Stege, Ulrike Langston, Michael A. |
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| Cites_doi | 10.1145/363958.363994 10.1145/800116.803771 10.1145/321879.321880 10.1145/322063.322075 10.1145/375360.375365 10.1002/j.1538-7305.1950.tb00463.x |
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| Keywords | Charge and reduce Fixed-parameter algorithm String-to-String Correction |
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| References_xml | – reference: L. Bergroth, H. Hakonen, T. Raita, A survey of longest common subsequence algorithms, in: Proc. 7th Int. Symp. on String Processing Information Retrieval, SPIRE’00, 2000. – volume: 38 start-page: 374 year: 2001 end-page: 410 ident: br000050 article-title: An efficient exact algorithm for constraint bipartite vertex cover publication-title: J. Algebra – volume: vol. 5532 start-page: 59 year: 2009 end-page: 70 ident: br000055 article-title: Searching trees: an essay publication-title: TAMC – volume: 7 year: 1964 ident: br000020 article-title: A technique for computer detection and correction of spelling errors publication-title: Commun. ACM – year: 1979 ident: br000040 article-title: Computers and Intractability: A Guide to the Theory of – volume: 29 start-page: 147 year: 1950 end-page: 160 ident: br000005 article-title: Error detecting and error correcting codes publication-title: Bell Syst. Tech. J. – volume: 33 year: 2001 ident: br000060 article-title: A guided tour to approximate string matching publication-title: ACM Comput. Surv. – volume: 25 start-page: 322 year: 1978 end-page: 336 ident: br000010 article-title: The complexity of some problems on subsequences and supersequences publication-title: J. ACM – year: 1966 ident: br000015 article-title: Binary codes capable of correcting deletions, insertions and reversals publication-title: Sov. Phys. Dokl. – volume: 22 start-page: 177 year: 1975 end-page: 183 ident: br000035 article-title: An extension of the string-to-string correction problem publication-title: J. ACM – reference: R.A. Wagner, On the complexity of the extended string-to-string correction problem, in: STOC’75, 1975, pp. 218–223. – year: 1999 ident: br000045 article-title: Parameterized Complexity – volume: 7 issue: 3 year: 1964 ident: 10.1016/j.disopt.2010.10.003_br000020 article-title: A technique for computer detection and correction of spelling errors publication-title: Commun. ACM doi: 10.1145/363958.363994 – volume: vol. 5532 start-page: 59 year: 2009 ident: 10.1016/j.disopt.2010.10.003_br000055 article-title: Searching trees: an essay – ident: 10.1016/j.disopt.2010.10.003_br000025 doi: 10.1145/800116.803771 – year: 1999 ident: 10.1016/j.disopt.2010.10.003_br000045 – volume: 38 start-page: 374 issue: 2 year: 2001 ident: 10.1016/j.disopt.2010.10.003_br000050 article-title: An efficient exact algorithm for constraint bipartite vertex cover publication-title: J. Algebra – year: 1966 ident: 10.1016/j.disopt.2010.10.003_br000015 article-title: Binary codes capable of correcting deletions, insertions and reversals publication-title: Sov. Phys. Dokl. – volume: 22 start-page: 177 year: 1975 ident: 10.1016/j.disopt.2010.10.003_br000035 article-title: An extension of the string-to-string correction problem publication-title: J. ACM doi: 10.1145/321879.321880 – volume: 25 start-page: 322 issue: 2 year: 1978 ident: 10.1016/j.disopt.2010.10.003_br000010 article-title: The complexity of some problems on subsequences and supersequences publication-title: J. ACM doi: 10.1145/322063.322075 – volume: 33 year: 2001 ident: 10.1016/j.disopt.2010.10.003_br000060 article-title: A guided tour to approximate string matching publication-title: ACM Comput. Surv. doi: 10.1145/375360.375365 – year: 1979 ident: 10.1016/j.disopt.2010.10.003_br000040 – volume: 29 start-page: 147 issue: 2 year: 1950 ident: 10.1016/j.disopt.2010.10.003_br000005 article-title: Error detecting and error correcting codes publication-title: Bell Syst. Tech. J. doi: 10.1002/j.1538-7305.1950.tb00463.x – ident: 10.1016/j.disopt.2010.10.003_br000030 |
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| Title | Charge and reduce: A fixed-parameter algorithm for String-to-String Correction |
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