### Abstract

We study the complexity of a classical combinatorial problem of computing the period of a string.We investigate both the average- and the worst-case complexity of the problem. We deliver almost tight bounds for the average-case. We show that every algorithm computing the period must examine (formula presented) symbols of an input string of lengthm. On the other hand we present an algorithm that computes the period by examining on average (formula presented) symbols, where |Σ| ³ 2 stands for the input alphabet. We also present a deterministic algorithm that computes the period of a string usingm+O(m^{3/4}) comparisons. This is the first algorithm that have the worstcase complexity m + o(m)

Original language | English (US) |
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Title of host publication | Combinatorial Pattern Matching - 11th Annual Symposium, CPM 2000, Proceedings |

Editors | Raffaele Giancarlo, David Sankoff |

Publisher | Springer Verlag |

Pages | 412-422 |

Number of pages | 11 |

ISBN (Electronic) | 3540676333, 9783540676331 |

DOIs | |

State | Published - Jan 1 2000 |

Externally published | Yes |

Event | 11th Annual Symposium on Combinatorial Pattern Matching, CPM 2000 - Montreal, Canada Duration: Jun 21 2000 → Jun 23 2000 |

### 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 | 1848 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 11th Annual Symposium on Combinatorial Pattern Matching, CPM 2000 |
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Country | Canada |

City | Montreal |

Period | 6/21/00 → 6/23/00 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Combinatorial Pattern Matching - 11th Annual Symposium, CPM 2000, Proceedings*(pp. 412-422). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1848). Springer Verlag. https://doi.org/10.1007/3-540-45123-4_34