### Abstract

It is known that the length of the longest substring palindromes (LSPals) of a given string T of length n can be computed in O(n) time by Manacher's algorithm [J. ACM '75]. In this paper, we consider the problem of finding the LSPal after the string is edited. We present an algorithm that uses O(n) time and space for preprocessing, and answers the length of the LSPals in O(log(min{ω, log n})) time after single character substitution, insertion, or deletion, where ω denotes the number of distinct characters appearing in T. We also propose an algorithm that uses O(n) time and space for preprocessing, and answers the length of the LSPals in O(ℓ+log n) time, after an existing substring in T is replaced by a string of arbitrary length ℓ.

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 | 121-1214 |

Number of pages | 1094 |

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 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software

### Cite this

*29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018*(pp. 121-1214). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 105). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.CPM.2018.12