### Abstract

Consider the prefix matching problem: Given a pattern P of length m and a text T of length n, find for all positions i in T the longest prefix of P starting at i. We present a parallel algorithm for the prefix matching problem over general alphabets whose text search takes optimal O(α(m)) time and preprocessing takes optimal O(log log m) time, where α(m) is the inverse Ackermann function. An Ω(log log m) lower bound for the prefix matching problem is implied by the same lower bound for string matching. However, the lower bound is applied only to preprocessing of the pattern and the searching phase can be faster. We prove an Ω(α(m)) lower bound for any linear-work searching phase. Therefore our algorithm is work-time optimal in both preprocessing and text search. The idea of leftmost witnesses is introduced to obtain the algorithm.

Original language | English (US) |
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Title of host publication | Algorithms - ESA'94 - 2nd Annual European Symposium, Proceedings |

Editors | Jan van Leeuwen |

Publisher | Springer Verlag |

Pages | 471-482 |

Number of pages | 12 |

ISBN (Print) | 9783540584346 |

State | Published - Jan 1 1994 |

Externally published | Yes |

Event | 2nd Annual European Symposium on Algorithms, ESA 1994 - Utrecht, Netherlands Duration: Sep 26 1994 → Sep 28 1994 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 855 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 2nd Annual European Symposium on Algorithms, ESA 1994 |
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Country | Netherlands |

City | Utrecht |

Period | 9/26/94 → 9/28/94 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms - ESA'94 - 2nd Annual European Symposium, Proceedings*(pp. 471-482). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 855 LNCS). Springer Verlag.