### Abstract

A closed string is a string with a proper substring that occurs in the string as a prefix and a suffix, but not elsewhere. Closed strings were introduced by Fici (Proc. WORDS, 2011) as objects of combinatorial interest in the study of Trapezoidal and Sturmian words. In this paper we consider algorithms for computing closed factors (substrings) in strings, and in particular for greedily factorizing a string into a sequence of longest closed factors. We describe an algorithm for this problem that uses linear time and space. We then consider the related problem of computing, for every position in the string, the longest closed factor starting at that position. We describe a simple algorithm for the problem that runs in O(n log n/ log log n) time.

Original language | English |
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Title of host publication | Proceedings of the Prague Stringology Conference 2014, PSC 2014 |

Editors | Jan Holub, Jan Zd'arek |

Publisher | Prague Stringology Club |

Pages | 162-168 |

Number of pages | 7 |

ISBN (Electronic) | 9788001055472 |

Publication status | Published - Jan 1 2014 |

Event | 18th Prague Stringology Conference, PSC 2014 - Prague, Czech Republic Duration: Sep 1 2014 → Sep 3 2014 |

### Publication series

Name | Proceedings of the Prague Stringology Conference 2014, PSC 2014 |
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### Other

Other | 18th Prague Stringology Conference, PSC 2014 |
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Country | Czech Republic |

City | Prague |

Period | 9/1/14 → 9/3/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Proceedings of the Prague Stringology Conference 2014, PSC 2014*(pp. 162-168). (Proceedings of the Prague Stringology Conference 2014, PSC 2014). Prague Stringology Club.

**Closed factorization.** / Badkobeh, Golnaz; Bannai, Hideo; Goto, Keisuke; I, Tomohiro; Iliopoulos, Costas S.; Inenaga, Shunsuke; Puglisi, Simon J.; Sugimoto, Shiho.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Prague Stringology Conference 2014, PSC 2014.*Proceedings of the Prague Stringology Conference 2014, PSC 2014, Prague Stringology Club, pp. 162-168, 18th Prague Stringology Conference, PSC 2014, Prague, Czech Republic, 9/1/14.

}

TY - GEN

T1 - Closed factorization

AU - Badkobeh, Golnaz

AU - Bannai, Hideo

AU - Goto, Keisuke

AU - I, Tomohiro

AU - Iliopoulos, Costas S.

AU - Inenaga, Shunsuke

AU - Puglisi, Simon J.

AU - Sugimoto, Shiho

PY - 2014/1/1

Y1 - 2014/1/1

N2 - A closed string is a string with a proper substring that occurs in the string as a prefix and a suffix, but not elsewhere. Closed strings were introduced by Fici (Proc. WORDS, 2011) as objects of combinatorial interest in the study of Trapezoidal and Sturmian words. In this paper we consider algorithms for computing closed factors (substrings) in strings, and in particular for greedily factorizing a string into a sequence of longest closed factors. We describe an algorithm for this problem that uses linear time and space. We then consider the related problem of computing, for every position in the string, the longest closed factor starting at that position. We describe a simple algorithm for the problem that runs in O(n log n/ log log n) time.

AB - A closed string is a string with a proper substring that occurs in the string as a prefix and a suffix, but not elsewhere. Closed strings were introduced by Fici (Proc. WORDS, 2011) as objects of combinatorial interest in the study of Trapezoidal and Sturmian words. In this paper we consider algorithms for computing closed factors (substrings) in strings, and in particular for greedily factorizing a string into a sequence of longest closed factors. We describe an algorithm for this problem that uses linear time and space. We then consider the related problem of computing, for every position in the string, the longest closed factor starting at that position. We describe a simple algorithm for the problem that runs in O(n log n/ log log n) time.

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UR - http://www.scopus.com/inward/citedby.url?scp=84928791807&partnerID=8YFLogxK

M3 - Conference contribution

T3 - Proceedings of the Prague Stringology Conference 2014, PSC 2014

SP - 162

EP - 168

BT - Proceedings of the Prague Stringology Conference 2014, PSC 2014

A2 - Holub, Jan

A2 - Zd'arek, Jan

PB - Prague Stringology Club

ER -