### Abstract

Strings u, v are said to be Abelian equivalent if u is a permutation of the characters appearing in v. A string w is said to have a full Abelian period p if w = w_{1} …w_{k}, where all wi’s are of length p each and are all Abelian equivalent. This paper studies reverse-engineering problems on full Abelian periods. Given a positive integer n and a set D of divisors of n, we show how to compute in O(n) time the lexicographically smallest string of length n which has all elements of D as its full Abelian periods and has the minimum number of full Abelian periods not in D. Moreover, we give an algorithm to enumerate all such strings in amortized constant time per output after O(n)-time preprocessing. Also, we show how to enumerate the strings which have all elements of D as its full Abelian periods in amortized constant time per output after O(n)-time preprocessing.

Original language | English |
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Title of host publication | Algorithms and Computation - 26th International Symposium, ISAAC 2015, Proceedings |

Editors | Khaled Elbassioni, Kazuhisa Makino |

Publisher | Springer Verlag |

Pages | 768-779 |

Number of pages | 12 |

ISBN (Print) | 9783662489703 |

DOIs | |

Publication status | Published - Jan 1 2015 |

Event | 26th International Symposium on Algorithms and Computation, ISAAC 2015 - Nagoya, Japan Duration: Dec 9 2015 → Dec 11 2015 |

### 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 | 9472 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 26th International Symposium on Algorithms and Computation, ISAAC 2015 |
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Country | Japan |

City | Nagoya |

Period | 12/9/15 → 12/11/15 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithms and Computation - 26th International Symposium, ISAAC 2015, Proceedings*(pp. 768-779). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9472). Springer Verlag. https://doi.org/10.1007/978-3-662-48971-0_64

**Inferring strings from full abelian periods.** / Nishida, Makoto; I, Tomohiro; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

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

*Algorithms and Computation - 26th International Symposium, ISAAC 2015, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9472, Springer Verlag, pp. 768-779, 26th International Symposium on Algorithms and Computation, ISAAC 2015, Nagoya, Japan, 12/9/15. https://doi.org/10.1007/978-3-662-48971-0_64

}

TY - GEN

T1 - Inferring strings from full abelian periods

AU - Nishida, Makoto

AU - I, Tomohiro

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Strings u, v are said to be Abelian equivalent if u is a permutation of the characters appearing in v. A string w is said to have a full Abelian period p if w = w1 …wk, where all wi’s are of length p each and are all Abelian equivalent. This paper studies reverse-engineering problems on full Abelian periods. Given a positive integer n and a set D of divisors of n, we show how to compute in O(n) time the lexicographically smallest string of length n which has all elements of D as its full Abelian periods and has the minimum number of full Abelian periods not in D. Moreover, we give an algorithm to enumerate all such strings in amortized constant time per output after O(n)-time preprocessing. Also, we show how to enumerate the strings which have all elements of D as its full Abelian periods in amortized constant time per output after O(n)-time preprocessing.

AB - Strings u, v are said to be Abelian equivalent if u is a permutation of the characters appearing in v. A string w is said to have a full Abelian period p if w = w1 …wk, where all wi’s are of length p each and are all Abelian equivalent. This paper studies reverse-engineering problems on full Abelian periods. Given a positive integer n and a set D of divisors of n, we show how to compute in O(n) time the lexicographically smallest string of length n which has all elements of D as its full Abelian periods and has the minimum number of full Abelian periods not in D. Moreover, we give an algorithm to enumerate all such strings in amortized constant time per output after O(n)-time preprocessing. Also, we show how to enumerate the strings which have all elements of D as its full Abelian periods in amortized constant time per output after O(n)-time preprocessing.

UR - http://www.scopus.com/inward/record.url?scp=84951950947&partnerID=8YFLogxK

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U2 - 10.1007/978-3-662-48971-0_64

DO - 10.1007/978-3-662-48971-0_64

M3 - Conference contribution

AN - SCOPUS:84951950947

SN - 9783662489703

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 768

EP - 779

BT - Algorithms and Computation - 26th International Symposium, ISAAC 2015, Proceedings

A2 - Elbassioni, Khaled

A2 - Makino, Kazuhisa

PB - Springer Verlag

ER -