### Abstract

The problem of finding all occurrences of a pattern of length m in a text of length n is considered. It is shown that the Boyer-Moore string matching algorithm performs roughly 3n comparisons and that this bound is tight up to O(n/m); more precisely, an upper bound of 3n-3(n-m+1)/(m+2) comparisons is shown, as is a lower bound of 3n(1-o(1)) comparisons, as n/m→∞ and m→∞. While the upper bound is somewhat involved, its main elements provide a simple proof of a 4n upper bound for the same algorithm.

Original language | English (US) |
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Pages (from-to) | 1075-1091 |

Number of pages | 17 |

Journal | SIAM Journal on Computing |

Volume | 23 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1 1994 |

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### ASJC Scopus subject areas

- Computer Science(all)
- Mathematics(all)