## Abstract

A string S of length n has period P of length p if S[i] = S[i+p] for all 1 ≤ i ≤ n−p and n ≥ 2p. The shortest such substring, P, is called the period of S, and the string S is called periodic in P. In this paper we investigate the period recovery problem. Given a string S of length n, find the primitive period(s) P such that the distance between S and the string that is periodic in P is below a threshold τ. We consider the period recovery problem over both the Hamming distance and the edit distance. For the Hamming distance case, we present an O(n log n) time algorithm, where τ is given as (Formula Presented), for 0 < ε < 1. For the edit distance case, (Formula Presented), and we provide an O(n^{4/3}) time algorithm.

Original language | English |
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Title of host publication | LATIN 2016 |

Subtitle of host publication | Theoretical Informatics - 12th Latin American Symposium, Proceedings |

Editors | Gonzalo Navarro, Evangelos Kranakis, Edgar Chávez |

Publisher | Springer Verlag |

Pages | 55-67 |

Number of pages | 13 |

ISBN (Print) | 9783662495285 |

DOIs | |

State | Published - 2016 |

Event | 12th Latin American Symposium on Theoretical Informatics, LATIN 2016 - Ensenada, Mexico Duration: 11 Apr 2016 → 15 Apr 2016 |

### 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 | 9644 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 12th Latin American Symposium on Theoretical Informatics, LATIN 2016 |
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Country/Territory | Mexico |

City | Ensenada |

Period | 11/04/16 → 15/04/16 |

### Bibliographical note

Funding Information:D. Sokol—Partially supported by the United States-Israel Binational Science Foundation (BSF) grant No. 2014028.

Funding Information:

M. Amit—Partially supported by the Israel Science Foundation grant 571/14, grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF) and DFG.

Funding Information:

A. Amir—Partially supported by the Israel Science Foundation grant 571/14, and grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF).

Publisher Copyright:

© Springer International Publishing Switzerland 2016.

## Keywords

- Approximate periodicity
- Edit distance
- Hamming distance
- Period recovery

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science (all)