## Abstract

Approximate matching is one of the fundamental problems in pattern matching, and a ubiquitous problem in real applications. The Hamming distance is a simple and well studied example of approximate matching, motivated by typing, or noisy channels. Biological and image processing applications assign a different value to mismatches of different symbols. We consider the problem of approximate matching in the L_{1} metric - the k-L_{1}-distance problem. Given text T = to, ..., t_{n-1} and pattern P = p_{o}, ..., p_{m-1} strings of natural number, and a natural number k, we seek all text locations i where the L_{1} distance of the pattern from the length m substring of text starting at i is not greater than k, i.e. ∑_{j=0}^{m-1} |t_{i+j}-p_{j}| ≤ k. We provide an algorithm that solves the k-L_{1} -distance problem in time O(n √k log k). The algorithm applies a bounded divide-and-conquer approach and makes noveluses of non-boolean convolutions.

Original language | English |
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Pages (from-to) | 91-103 |

Number of pages | 13 |

Journal | Lecture Notes in Computer Science |

Volume | 3537 |

DOIs | |

State | Published - 2005 |

Event | Ot16th Annual Symposium on Combinatorial Pattern Matching, CPM 2005 - Jeju Island, Korea, Republic of Duration: 19 Jun 2005 → 22 Jun 2005 |

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