### Abstract

The longest Lyndon substring of a string T is the longest substring of T which is a Lyndon word. LLS(T) denotes the length of the longest Lyndon substring of a string T. In this paper, we consider computing LLS(T′) where T′ is an edited string formed from T. After O(n) time and space preprocessing, our algorithm returns LLS(T′) in O(log n) time for any single character edit. We also consider a version of the problem with block edits, i.e., a substring of T is replaced by a given string of length l. After O(n) time and space preprocessing, our algorithm returns LLS(T′) in O(l log σ + log n) time for any block edit where σ is the number of distinct characters in T. We can modify our algorithm so as to output all the longest Lyndon substrings of T′ for both problems.

Original language | English |
---|---|

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 | 191-1910 |

Number of pages | 1720 |

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 |
---|---|

Volume | 105 |

ISSN (Print) | 1868-8969 |

### Other

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

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. 191-1910). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 105). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.CPM.2018.19

**Longest lyndon substring after edit.** / Urabe, Yuki; Nakashima, Yuto; Inenaga, Shunsuke; 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. 191-1910, 29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018, Qingdao, China, 7/2/18. https://doi.org/10.4230/LIPIcs.CPM.2018.19

}

TY - GEN

T1 - Longest lyndon substring after edit

AU - Urabe, Yuki

AU - Nakashima, Yuto

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2018/5/1

Y1 - 2018/5/1

N2 - The longest Lyndon substring of a string T is the longest substring of T which is a Lyndon word. LLS(T) denotes the length of the longest Lyndon substring of a string T. In this paper, we consider computing LLS(T′) where T′ is an edited string formed from T. After O(n) time and space preprocessing, our algorithm returns LLS(T′) in O(log n) time for any single character edit. We also consider a version of the problem with block edits, i.e., a substring of T is replaced by a given string of length l. After O(n) time and space preprocessing, our algorithm returns LLS(T′) in O(l log σ + log n) time for any block edit where σ is the number of distinct characters in T. We can modify our algorithm so as to output all the longest Lyndon substrings of T′ for both problems.

AB - The longest Lyndon substring of a string T is the longest substring of T which is a Lyndon word. LLS(T) denotes the length of the longest Lyndon substring of a string T. In this paper, we consider computing LLS(T′) where T′ is an edited string formed from T. After O(n) time and space preprocessing, our algorithm returns LLS(T′) in O(log n) time for any single character edit. We also consider a version of the problem with block edits, i.e., a substring of T is replaced by a given string of length l. After O(n) time and space preprocessing, our algorithm returns LLS(T′) in O(l log σ + log n) time for any block edit where σ is the number of distinct characters in T. We can modify our algorithm so as to output all the longest Lyndon substrings of T′ for both problems.

UR - http://www.scopus.com/inward/record.url?scp=85048299606&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048299606&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.CPM.2018.19

DO - 10.4230/LIPIcs.CPM.2018.19

M3 - Conference contribution

AN - SCOPUS:85048299606

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 191

EP - 1910

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 -