### Abstract

Original language | English |
---|---|

Pages (from-to) | 41-49 |

Number of pages | 9 |

Journal | Discrete Optimization |

Volume | 8 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2011 |

Externally published | Yes |

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### Cite this

*Discrete Optimization*,

*8*(1), 41-49. https://doi.org/10.1016/j.disopt.2010.10.003

}

*Discrete Optimization*, vol. 8, no. 1, pp. 41-49. https://doi.org/10.1016/j.disopt.2010.10.003

**Charge and reduce : A fixed-parameter algorithm for String-to-String Correction.** / Abu Khzam, Faisal; Fernau, Henning; Langston, M; Lee-Cultura, S; Stege, Ulrike.

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

TY - JOUR

T1 - Charge and reduce

T2 - A fixed-parameter algorithm for String-to-String Correction

AU - Abu Khzam, Faisal

AU - Fernau, Henning

AU - Langston, M

AU - Lee-Cultura, S

AU - Stege, Ulrike

PY - 2011

Y1 - 2011

N2 - 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 NPcomplete 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 fixedparameter tractable, for parameter k, and present a simple fixed-parameter algorithm that solves the problem in O(2kn) 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(1.6181kn).

AB - 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 NPcomplete 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 fixedparameter tractable, for parameter k, and present a simple fixed-parameter algorithm that solves the problem in O(2kn) 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(1.6181kn).

U2 - 10.1016/j.disopt.2010.10.003

DO - 10.1016/j.disopt.2010.10.003

M3 - Article

VL - 8

SP - 41

EP - 49

JO - Discrete Optimization

JF - Discrete Optimization

SN - 1572-5286

IS - 1

ER -