### Abstract

Two strings X and Y are considered Abelian equal if the letters of X can be permuted to obtain Y (and vice versa). Recently, Alatabbi et al. (2015) considered the longest common Abelian factor problem in which we are asked to find the length of the longest Abelian-equal factor present in a given pair of strings. They provided an algorithm that uses O(σn^{2}) time and O(σn) space, where n is the length of the pair of strings and σ is the alphabet size. In this paper we describe an algorithm that uses O(n^{2} log^{2} n log∗ n) time and O(n log^{2} n) space, significantly improving Alatabbi et al.’s result unless the alphabet is small. Our algorithm makes use of techniques for maintaining a dynamic set of strings under split, join, and equality testing (Melhorn et al., Algorithmica 17(2), 1997).

Original language | English |
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Title of host publication | String Processing and Information Retrieval - 23rd International Symposium, SPIRE 2016, Proceedings |

Editors | Shunsuke Inenaga, Kunihiko Sadakane, Tetsuya Sakai |

Publisher | Springer Verlag |

Pages | 254-259 |

Number of pages | 6 |

ISBN (Print) | 9783319460482 |

DOIs | |

Publication status | Published - Jan 1 2016 |

Event | 23rd International Symposium on String Processing and Information Retrieval, SPIRE 2016 - Beppu, Japan Duration: Oct 18 2016 → Oct 20 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 | 9954 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 23rd International Symposium on String Processing and Information Retrieval, SPIRE 2016 |
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Country | Japan |

City | Beppu |

Period | 10/18/16 → 10/20/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*String Processing and Information Retrieval - 23rd International Symposium, SPIRE 2016, Proceedings*(pp. 254-259). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9954 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-46049-9_24

**Longest common Abelian factors and large alphabets.** / Badkobeh, Golnaz; Gagie, Travis; Grabowski, Szymon; Nakashima, Yuto; Puglisi, Simon J.; Sugimoto, Shiho.

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

*String Processing and Information Retrieval - 23rd International Symposium, SPIRE 2016, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9954 LNCS, Springer Verlag, pp. 254-259, 23rd International Symposium on String Processing and Information Retrieval, SPIRE 2016, Beppu, Japan, 10/18/16. https://doi.org/10.1007/978-3-319-46049-9_24

}

TY - GEN

T1 - Longest common Abelian factors and large alphabets

AU - Badkobeh, Golnaz

AU - Gagie, Travis

AU - Grabowski, Szymon

AU - Nakashima, Yuto

AU - Puglisi, Simon J.

AU - Sugimoto, Shiho

PY - 2016/1/1

Y1 - 2016/1/1

N2 - Two strings X and Y are considered Abelian equal if the letters of X can be permuted to obtain Y (and vice versa). Recently, Alatabbi et al. (2015) considered the longest common Abelian factor problem in which we are asked to find the length of the longest Abelian-equal factor present in a given pair of strings. They provided an algorithm that uses O(σn2) time and O(σn) space, where n is the length of the pair of strings and σ is the alphabet size. In this paper we describe an algorithm that uses O(n2 log2 n log∗ n) time and O(n log2 n) space, significantly improving Alatabbi et al.’s result unless the alphabet is small. Our algorithm makes use of techniques for maintaining a dynamic set of strings under split, join, and equality testing (Melhorn et al., Algorithmica 17(2), 1997).

AB - Two strings X and Y are considered Abelian equal if the letters of X can be permuted to obtain Y (and vice versa). Recently, Alatabbi et al. (2015) considered the longest common Abelian factor problem in which we are asked to find the length of the longest Abelian-equal factor present in a given pair of strings. They provided an algorithm that uses O(σn2) time and O(σn) space, where n is the length of the pair of strings and σ is the alphabet size. In this paper we describe an algorithm that uses O(n2 log2 n log∗ n) time and O(n log2 n) space, significantly improving Alatabbi et al.’s result unless the alphabet is small. Our algorithm makes use of techniques for maintaining a dynamic set of strings under split, join, and equality testing (Melhorn et al., Algorithmica 17(2), 1997).

UR - http://www.scopus.com/inward/record.url?scp=84989948571&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84989948571&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-46049-9_24

DO - 10.1007/978-3-319-46049-9_24

M3 - Conference contribution

AN - SCOPUS:84989948571

SN - 9783319460482

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

SP - 254

EP - 259

BT - String Processing and Information Retrieval - 23rd International Symposium, SPIRE 2016, Proceedings

A2 - Inenaga, Shunsuke

A2 - Sadakane, Kunihiko

A2 - Sakai, Tetsuya

PB - Springer Verlag

ER -