## Abstract

Let a text T = t_{0}, ..., t_{n - 1} and a pattern P = p_{0}, ..., p_{m - 1}, strings of natural numbers, be given. In the Approximate Matching in theL_{∞} metric problem the output is, for every text location i, the L_{∞} distance between the pattern and the length m substring of the text starting at i, i.e., Max_{j = 0}^{m - 1} | t_{i + j} - p_{j} |. We consider the Approximatek - L_{∞} distance problem. Given text T and pattern P as before, and a natural number k the output of the problem is the L_{∞} distance of the pattern from the text only at locations i in the text where the distance is bounded by k. For the locations where the distance exceeds k the output is φ{symbol}. We show an algorithm that solves this problem in O (n (k + log (min (m, | Σ |))) log m) time.

Original language | English |
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Pages (from-to) | 138-140 |

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

## Keywords

- Analysis of algorithms
- Approximation algorithms
- Pattern matching
- Time series analysis

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