### Abstract

A square is a non-empty string of form Y Y. The longest common square subsequence (LCSqS) problem is to compute a longest square occurring as a subsequence in two given strings A and B. We show that the problem can easily be solved in O(n^{6}) time or O(|M|n^{4}) time with O(n^{4}) space, where n is the length of the strings and M is the set of matching points between A and B. Then, we show that the problem can also be solved in O(σ|M|^{3} + n) time and O(|M|^{2} + n) space, or in O(|M|^{3} log^{2} n log log n + n) time with O(|M|^{3} + n) space, where σ is the number of distinct characters occurring in A and B. We also study lower bounds for the LCSqS problem for two or more strings.

Original language | English |
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Title of host publication | 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018 |

Editors | Binhai Zhu, Gonzalo Navarro, David Sankoff |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

Pages | 151-1513 |

Number of pages | 1363 |

ISBN (Electronic) | 9783959770743 |

DOIs | |

Publication status | Published - May 1 2018 |

Event | 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018 - Qingdao, China Duration: Jul 2 2018 → Jul 4 2018 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 105 |

ISSN (Print) | 1868-8969 |

### Other

Other | 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018 |
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Country | China |

City | Qingdao |

Period | 7/2/18 → 7/4/18 |

### All Science Journal Classification (ASJC) codes

- Software

### Cite this

*29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018*(pp. 151-1513). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 105). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.CPM.2018.15

**Computing longest common square subsequences.** / Inoue, Takafumi; Inenaga, Shunsuke; Hyyrö, Heikki; Bannai, Hideo; Takeda, Masayuki.

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

*29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018.*Leibniz International Proceedings in Informatics, LIPIcs, vol. 105, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, pp. 151-1513, 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018, Qingdao, China, 7/2/18. https://doi.org/10.4230/LIPIcs.CPM.2018.15

}

TY - GEN

T1 - Computing longest common square subsequences

AU - Inoue, Takafumi

AU - Inenaga, Shunsuke

AU - Hyyrö, Heikki

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2018/5/1

Y1 - 2018/5/1

N2 - A square is a non-empty string of form Y Y. The longest common square subsequence (LCSqS) problem is to compute a longest square occurring as a subsequence in two given strings A and B. We show that the problem can easily be solved in O(n6) time or O(|M|n4) time with O(n4) space, where n is the length of the strings and M is the set of matching points between A and B. Then, we show that the problem can also be solved in O(σ|M|3 + n) time and O(|M|2 + n) space, or in O(|M|3 log2 n log log n + n) time with O(|M|3 + n) space, where σ is the number of distinct characters occurring in A and B. We also study lower bounds for the LCSqS problem for two or more strings.

AB - A square is a non-empty string of form Y Y. The longest common square subsequence (LCSqS) problem is to compute a longest square occurring as a subsequence in two given strings A and B. We show that the problem can easily be solved in O(n6) time or O(|M|n4) time with O(n4) space, where n is the length of the strings and M is the set of matching points between A and B. Then, we show that the problem can also be solved in O(σ|M|3 + n) time and O(|M|2 + n) space, or in O(|M|3 log2 n log log n + n) time with O(|M|3 + n) space, where σ is the number of distinct characters occurring in A and B. We also study lower bounds for the LCSqS problem for two or more strings.

UR - http://www.scopus.com/inward/record.url?scp=85048306163&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048306163&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.CPM.2018.15

DO - 10.4230/LIPIcs.CPM.2018.15

M3 - Conference contribution

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 151

EP - 1513

BT - 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018

A2 - Zhu, Binhai

A2 - Navarro, Gonzalo

A2 - Sankoff, David

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

ER -