### Abstract

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

Journal | Journal of Algorithms |

Volume | 56 |

Pages (from-to) | 124-153 |

Number of pages | 30 |

ISSN | 0196-6774 |

DOIs | |

Publication status | Published - 2005 |

MoE publication type | A1 Journal article-refereed |

### Fields of Science

- 113 Computer and information sciences

### Cite this

*Journal of Algorithms*,

*56*, 124-153. https://doi.org/10.1016/j.jgalgot.2004.07.008

}

*Journal of Algorithms*, vol. 56, pp. 124-153. https://doi.org/10.1016/j.jgalgot.2004.07.008

**Transposition invariant string matching.** / Mäkinen, Veli; Navarro, Gonzalo; Ukkonen, Esko.

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

TY - JOUR

T1 - Transposition invariant string matching

AU - Mäkinen, Veli

AU - Navarro, Gonzalo

AU - Ukkonen, Esko

PY - 2005

Y1 - 2005

N2 - Given strings A = a(1)a(2)...a(m) and B=b(1)b(2)...b(n) over an alphabet Sigma subset of U, where U is some numerical universe closed under addition and subtraction, and a distance function d(A, B) that gives the score of the best (partial) matching of A and B, the transposition invariant distance is min(t is an element of U){d(A + t, B)}, where A + t = (a(1) + t)(a(2) + t)...(a(m) + t). We study the problem of computing the transposition invariant distance for various distance (and similarity) functions d, including Hamming distance, longest common subsequence (LCS), Levenshtein distance, and their versions where the exact matching condition is replaced by an approximate one. For all these problems we give algorithms whose time complexities are close to the known upper bounds without transposition invariance, and for some we achieve these upper bounds. In particular, we show how sparse dynamic programming can be used to solve transposition invariant problems, and its connection with multidimensional range-minimum search. As a byproduct, we give improved sparse dynamic programming algorithms to compute LCS and Levenshtein distance. (c) 2004 Elsevier Inc. All rights reserved.

AB - Given strings A = a(1)a(2)...a(m) and B=b(1)b(2)...b(n) over an alphabet Sigma subset of U, where U is some numerical universe closed under addition and subtraction, and a distance function d(A, B) that gives the score of the best (partial) matching of A and B, the transposition invariant distance is min(t is an element of U){d(A + t, B)}, where A + t = (a(1) + t)(a(2) + t)...(a(m) + t). We study the problem of computing the transposition invariant distance for various distance (and similarity) functions d, including Hamming distance, longest common subsequence (LCS), Levenshtein distance, and their versions where the exact matching condition is replaced by an approximate one. For all these problems we give algorithms whose time complexities are close to the known upper bounds without transposition invariance, and for some we achieve these upper bounds. In particular, we show how sparse dynamic programming can be used to solve transposition invariant problems, and its connection with multidimensional range-minimum search. As a byproduct, we give improved sparse dynamic programming algorithms to compute LCS and Levenshtein distance. (c) 2004 Elsevier Inc. All rights reserved.

KW - 113 Computer and information sciences

U2 - 10.1016/j.jgalgot.2004.07.008

DO - 10.1016/j.jgalgot.2004.07.008

M3 - Article

VL - 56

SP - 124

EP - 153

JO - Journal of Algorithms

JF - Journal of Algorithms

SN - 0196-6774

ER -