### Abstract

A string s is said to be a gapped palindrome iff s = xyx^{R}for some strings x, y such that |x| ≥ 1, |y| ≥ 2, and xR denotes the reverse image of x.In this paper we consider two kinds of gapped palindromes, and present efficient online algorithms to compute these gapped palindromes occurring in a string.First, we show an online algorithm to find all maximal g-gapped palindromes with fixed gap length g ≥ 2 in a string of length n in O(n log σ) time and O(n) space, where σ is the alphabet size.Second, we show an online algorithm to find all maximal lengthconstrained gapped palindromes with arm length at least A ≥ 1 and gap length in range [g_{min}, g_{max}] in O (formula presented) time and O(n) space.We also show that if A is a constant, then there exists a string of length n which contains Ω(n(g_{max}− g_{min})) maximal LCGPs, which implies we cannot hope for a significant speed-up in the worst case.

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

Title of host publication | Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings |

Editors | Veli Mäkinen, Simon J. Puglisi, Leena Salmela |

Publisher | Springer Verlag |

Pages | 191-202 |

Number of pages | 12 |

ISBN (Print) | 9783319445427 |

DOIs | |

Publication status | Published - Jan 1 2016 |

Event | 27th International Workshop on Combinatorial Algorithms, IWOCA 2016 - Helsinki, Finland Duration: Aug 17 2016 → Aug 19 2016 |

### Publication series

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

Volume | 9843 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 27th International Workshop on Combinatorial Algorithms, IWOCA 2016 |
---|---|

Country | Finland |

City | Helsinki |

Period | 8/17/16 → 8/19/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings*(pp. 191-202). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9843 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-44543-4_15

**Finding gapped palindromes online.** / Fujishige, Yuta; Nakamura, Michitaro; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

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

*Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9843 LNCS, Springer Verlag, pp. 191-202, 27th International Workshop on Combinatorial Algorithms, IWOCA 2016, Helsinki, Finland, 8/17/16. https://doi.org/10.1007/978-3-319-44543-4_15

}

TY - GEN

T1 - Finding gapped palindromes online

AU - Fujishige, Yuta

AU - Nakamura, Michitaro

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2016/1/1

Y1 - 2016/1/1

N2 - A string s is said to be a gapped palindrome iff s = xyxRfor some strings x, y such that |x| ≥ 1, |y| ≥ 2, and xR denotes the reverse image of x.In this paper we consider two kinds of gapped palindromes, and present efficient online algorithms to compute these gapped palindromes occurring in a string.First, we show an online algorithm to find all maximal g-gapped palindromes with fixed gap length g ≥ 2 in a string of length n in O(n log σ) time and O(n) space, where σ is the alphabet size.Second, we show an online algorithm to find all maximal lengthconstrained gapped palindromes with arm length at least A ≥ 1 and gap length in range [gmin, gmax] in O (formula presented) time and O(n) space.We also show that if A is a constant, then there exists a string of length n which contains Ω(n(gmax− gmin)) maximal LCGPs, which implies we cannot hope for a significant speed-up in the worst case.

AB - A string s is said to be a gapped palindrome iff s = xyxRfor some strings x, y such that |x| ≥ 1, |y| ≥ 2, and xR denotes the reverse image of x.In this paper we consider two kinds of gapped palindromes, and present efficient online algorithms to compute these gapped palindromes occurring in a string.First, we show an online algorithm to find all maximal g-gapped palindromes with fixed gap length g ≥ 2 in a string of length n in O(n log σ) time and O(n) space, where σ is the alphabet size.Second, we show an online algorithm to find all maximal lengthconstrained gapped palindromes with arm length at least A ≥ 1 and gap length in range [gmin, gmax] in O (formula presented) time and O(n) space.We also show that if A is a constant, then there exists a string of length n which contains Ω(n(gmax− gmin)) maximal LCGPs, which implies we cannot hope for a significant speed-up in the worst case.

UR - http://www.scopus.com/inward/record.url?scp=84984908030&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84984908030&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-44543-4_15

DO - 10.1007/978-3-319-44543-4_15

M3 - Conference contribution

SN - 9783319445427

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

SP - 191

EP - 202

BT - Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings

A2 - Mäkinen, Veli

A2 - Puglisi, Simon J.

A2 - Salmela, Leena

PB - Springer Verlag

ER -