## Abstract

Let a text string T = t_{0}, ..., t_{n - 1} and a pattern string P = p_{0}, ..., p_{m - 1}, t_{i}, p_{j} ∈ N be given. In the Approximate Pattern Matching in theL_{1} metric problem (L_{1}-matching for short) the output is, for every text location i, the L_{1} distance between the pattern and the length m substring of the text starting at i, i.e. ∑_{j = 0}^{m - 1} | t_{i + j} - p_{j} |. The Less Than Matching problem is that of finding all locations i of T where t_{i + j} ≥ p_{j}, j = 0, ..., m - 1. The String Matching with Mismatches problem is that of finding the number of mismatches between the pattern and every length m substring of the text. For the three above problems, the fastest known deterministic solution is O (n sqrt(m log m)) time. In this paper we show that the latter two problems can be linearly reduced to the problem of L_{1}-matching.

Original language | English |
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Pages (from-to) | 141-143 |

Number of pages | 3 |

Journal | Information Processing Letters |

Volume | 105 |

Issue number | 4 |

DOIs | |

State | Published - 15 Feb 2008 |

### Bibliographical note

Funding Information:* Corresponding author. Tel.: +972 3 531 7620. E-mail addresses: ohadlipsky@yahoo.com (O. Lipsky), porately@cs.biu.ac.il (E. Porat). 1 Tel.: +972 3 531 8408. 2 Partially supported by GIF Young Scientists Program grant 2055-1168.6/2002.

## Keywords

- Analysis of algorithms
- Lower bound
- Pattern matching
- Time series analysis

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