### 抄録

A Longest Common Extension (LCE) query on a text T of length N asks for the length of the longest common prefix of suffixes starting at given two positions. We show that the signature encoding G of size w = O(min(z logN log∗M,N)) [Mehlhorn et al., Algorithmica 17(2):183- 198, 1997] of T, which can be seen as a compressed representation of T, has a capability to support LCE queries in O(logN + log ℓ log∗M) time, where ℓ is the answer to the query, z is the size of the Lempel-Ziv77 (LZ77) factorization of T, and M ≥ 4N is an integer that can be handled in constant time under word RAM model. In compressed space, this is the fastest deterministic LCE data structure in many cases. Moreover, G can be enhanced to support efficient update operations: After processing G in O(wfA) time, we can insert/delete any (sub)string of length y into/from an arbitrary position of T in O((y + logN log∗M)fA) time, where fA = O(min{log log M log log w/log log log M, √log w/log log w}). This yields the first fully dynamic LCE data structure working in compressed space. We also present efficient construction algorithms from various types of inputs: We can construct G in O(NfA) time from uncompressed string T; in O(n log log(n log∗M) logN log∗M) time from grammar-compressed string T represented by a straight-line program of size n; and in O(zfA logN log∗M) time from LZ77-compressed string T with z factors. On top of the above contributions, we show several applications of our data structures which improve previous best known results on grammar-compressed string processing.

元の言語 | 英語 |
---|---|

ホスト出版物のタイトル | 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 |

出版者 | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

巻 | 58 |

ISBN（電子版） | 9783959770163 |

DOI | |

出版物ステータス | 出版済み - 8 1 2016 |

イベント | 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 - Krakow, ポーランド 継続期間: 8 22 2016 → 8 26 2016 |

### その他

その他 | 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 |
---|---|

国 | ポーランド |

市 | Krakow |

期間 | 8/22/16 → 8/26/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software

### これを引用

*41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016*(巻 58). [72] Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.MFCS.2016.72

**Fully dynamic data structure for LCE queries in compressed space.** / Nishimoto, Takaaki; Tomohiro, I.; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

研究成果: 著書/レポートタイプへの貢献 › 会議での発言

*41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016.*巻. 58, 72, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016, Krakow, ポーランド, 8/22/16. https://doi.org/10.4230/LIPIcs.MFCS.2016.72

}

TY - GEN

T1 - Fully dynamic data structure for LCE queries in compressed space

AU - Nishimoto, Takaaki

AU - Tomohiro, I.

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2016/8/1

Y1 - 2016/8/1

N2 - A Longest Common Extension (LCE) query on a text T of length N asks for the length of the longest common prefix of suffixes starting at given two positions. We show that the signature encoding G of size w = O(min(z logN log∗M,N)) [Mehlhorn et al., Algorithmica 17(2):183- 198, 1997] of T, which can be seen as a compressed representation of T, has a capability to support LCE queries in O(logN + log ℓ log∗M) time, where ℓ is the answer to the query, z is the size of the Lempel-Ziv77 (LZ77) factorization of T, and M ≥ 4N is an integer that can be handled in constant time under word RAM model. In compressed space, this is the fastest deterministic LCE data structure in many cases. Moreover, G can be enhanced to support efficient update operations: After processing G in O(wfA) time, we can insert/delete any (sub)string of length y into/from an arbitrary position of T in O((y + logN log∗M)fA) time, where fA = O(min{log log M log log w/log log log M, √log w/log log w}). This yields the first fully dynamic LCE data structure working in compressed space. We also present efficient construction algorithms from various types of inputs: We can construct G in O(NfA) time from uncompressed string T; in O(n log log(n log∗M) logN log∗M) time from grammar-compressed string T represented by a straight-line program of size n; and in O(zfA logN log∗M) time from LZ77-compressed string T with z factors. On top of the above contributions, we show several applications of our data structures which improve previous best known results on grammar-compressed string processing.

AB - A Longest Common Extension (LCE) query on a text T of length N asks for the length of the longest common prefix of suffixes starting at given two positions. We show that the signature encoding G of size w = O(min(z logN log∗M,N)) [Mehlhorn et al., Algorithmica 17(2):183- 198, 1997] of T, which can be seen as a compressed representation of T, has a capability to support LCE queries in O(logN + log ℓ log∗M) time, where ℓ is the answer to the query, z is the size of the Lempel-Ziv77 (LZ77) factorization of T, and M ≥ 4N is an integer that can be handled in constant time under word RAM model. In compressed space, this is the fastest deterministic LCE data structure in many cases. Moreover, G can be enhanced to support efficient update operations: After processing G in O(wfA) time, we can insert/delete any (sub)string of length y into/from an arbitrary position of T in O((y + logN log∗M)fA) time, where fA = O(min{log log M log log w/log log log M, √log w/log log w}). This yields the first fully dynamic LCE data structure working in compressed space. We also present efficient construction algorithms from various types of inputs: We can construct G in O(NfA) time from uncompressed string T; in O(n log log(n log∗M) logN log∗M) time from grammar-compressed string T represented by a straight-line program of size n; and in O(zfA logN log∗M) time from LZ77-compressed string T with z factors. On top of the above contributions, we show several applications of our data structures which improve previous best known results on grammar-compressed string processing.

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U2 - 10.4230/LIPIcs.MFCS.2016.72

DO - 10.4230/LIPIcs.MFCS.2016.72

M3 - Conference contribution

VL - 58

BT - 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016

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

ER -