### Abstract

palindrome is a string that reads the same forward and backward. A palindromic substring P of a string S is called a shortest unique palindromic substring (SUPS) for an interval [s, t] in S, if P occurs exactly once in S, this occurrence of P contains interval [s, t], and every palindromic substring of S which contains interval [s, t] and is shorter than P occurs at least twice in S. The SUPS problem is, given a string S, to preprocess S so that for any subsequent query interval [s, t] all the SUPSs for interval [s, t] can be answered quickly. We present an optimal solution to this problem. Namely, we show how to preprocess a given string S of length n in O(n) time and space so that all SUPSs for any subsequent query interval can be answered in O(α + 1) time, where α is the number of outputs.

Original language | English |
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Title of host publication | Combinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers |

Editors | William F. Smyth, Ljiljana Brankovic, Joe Ryan |

Publisher | Springer Verlag |

Pages | 397-408 |

Number of pages | 12 |

ISBN (Print) | 9783319788241 |

DOIs | |

Publication status | Published - Jan 1 2018 |

Event | 28th International Workshop on Combinational Algorithms, IWOCA 2017 - Newcastle, NSW, Australia Duration: Jul 17 2017 → Jul 21 2017 |

### 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 | 10765 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 28th International Workshop on Combinational Algorithms, IWOCA 2017 |
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Country | Australia |

City | Newcastle, NSW |

Period | 7/17/17 → 7/21/17 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Combinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers*(pp. 397-408). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10765 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-78825-8_32

**Shortest unique palindromic substring queries in optimal time.** / Nakashima, Yuto; Inoue, Hiroe; Mieno, Takuya; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

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

*Combinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10765 LNCS, Springer Verlag, pp. 397-408, 28th International Workshop on Combinational Algorithms, IWOCA 2017, Newcastle, NSW, Australia, 7/17/17. https://doi.org/10.1007/978-3-319-78825-8_32

}

TY - GEN

T1 - Shortest unique palindromic substring queries in optimal time

AU - Nakashima, Yuto

AU - Inoue, Hiroe

AU - Mieno, Takuya

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2018/1/1

Y1 - 2018/1/1

N2 - palindrome is a string that reads the same forward and backward. A palindromic substring P of a string S is called a shortest unique palindromic substring (SUPS) for an interval [s, t] in S, if P occurs exactly once in S, this occurrence of P contains interval [s, t], and every palindromic substring of S which contains interval [s, t] and is shorter than P occurs at least twice in S. The SUPS problem is, given a string S, to preprocess S so that for any subsequent query interval [s, t] all the SUPSs for interval [s, t] can be answered quickly. We present an optimal solution to this problem. Namely, we show how to preprocess a given string S of length n in O(n) time and space so that all SUPSs for any subsequent query interval can be answered in O(α + 1) time, where α is the number of outputs.

AB - palindrome is a string that reads the same forward and backward. A palindromic substring P of a string S is called a shortest unique palindromic substring (SUPS) for an interval [s, t] in S, if P occurs exactly once in S, this occurrence of P contains interval [s, t], and every palindromic substring of S which contains interval [s, t] and is shorter than P occurs at least twice in S. The SUPS problem is, given a string S, to preprocess S so that for any subsequent query interval [s, t] all the SUPSs for interval [s, t] can be answered quickly. We present an optimal solution to this problem. Namely, we show how to preprocess a given string S of length n in O(n) time and space so that all SUPSs for any subsequent query interval can be answered in O(α + 1) time, where α is the number of outputs.

UR - http://www.scopus.com/inward/record.url?scp=85045984814&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85045984814&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-78825-8_32

DO - 10.1007/978-3-319-78825-8_32

M3 - Conference contribution

SN - 9783319788241

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

SP - 397

EP - 408

BT - Combinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers

A2 - Smyth, William F.

A2 - Brankovic, Ljiljana

A2 - Ryan, Joe

PB - Springer Verlag

ER -