### Abstract

For a set D of documents and a positive integer d, a string w is said to be d-left-right maximal, if (1) w occurs in at least d documents in D, and (2) any proper superstring of w occurs in less than d documents. The left-right-maximal generic words problem is, given a set D of documents, to preprocess D so that for any string p and for any positive integer d, all the superstrings of p that are d-left-right maximal can be answered quickly. In this paper, we present an O(n log m) space data structure (in words) which answers queries in O(|p| + o log log m) time, where n is the total length of documents in D, m is the number of documents in D and o is the number of outputs. Our solution improves the previous one by Nishimoto et al. (PSC 2015), which uses an O(n log n) space data structure answering queries in O(|p| + r · log n + o · log^{2} n) time, where r is the number of right-extensions q of p occurring in at least d documents such that any proper right extension of q occurs in less than d documents.

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

Title of host publication | 30th International Symposium on Algorithms and Computation, ISAAC 2019 |

Editors | Pinyan Lu, Guochuan Zhang |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959771306 |

DOIs | |

Publication status | Published - Dec 2019 |

Event | 30th International Symposium on Algorithms and Computation, ISAAC 2019 - Shanghai, China Duration: Dec 8 2019 → Dec 11 2019 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
---|---|

Volume | 149 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 30th International Symposium on Algorithms and Computation, ISAAC 2019 |
---|---|

Country | China |

City | Shanghai |

Period | 12/8/19 → 12/11/19 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software

### Cite this

*30th International Symposium on Algorithms and Computation, ISAAC 2019*[40] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 149). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ISAAC.2019.40

**An improved data structure for left-right maximal generic words problem.** / Fujishige, Yuta; Nakashima, Yuto; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

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

*30th International Symposium on Algorithms and Computation, ISAAC 2019.*, 40, Leibniz International Proceedings in Informatics, LIPIcs, vol. 149, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 30th International Symposium on Algorithms and Computation, ISAAC 2019, Shanghai, China, 12/8/19. https://doi.org/10.4230/LIPIcs.ISAAC.2019.40

}

TY - GEN

T1 - An improved data structure for left-right maximal generic words problem

AU - Fujishige, Yuta

AU - Nakashima, Yuto

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2019/12

Y1 - 2019/12

N2 - For a set D of documents and a positive integer d, a string w is said to be d-left-right maximal, if (1) w occurs in at least d documents in D, and (2) any proper superstring of w occurs in less than d documents. The left-right-maximal generic words problem is, given a set D of documents, to preprocess D so that for any string p and for any positive integer d, all the superstrings of p that are d-left-right maximal can be answered quickly. In this paper, we present an O(n log m) space data structure (in words) which answers queries in O(|p| + o log log m) time, where n is the total length of documents in D, m is the number of documents in D and o is the number of outputs. Our solution improves the previous one by Nishimoto et al. (PSC 2015), which uses an O(n log n) space data structure answering queries in O(|p| + r · log n + o · log2 n) time, where r is the number of right-extensions q of p occurring in at least d documents such that any proper right extension of q occurs in less than d documents.

AB - For a set D of documents and a positive integer d, a string w is said to be d-left-right maximal, if (1) w occurs in at least d documents in D, and (2) any proper superstring of w occurs in less than d documents. The left-right-maximal generic words problem is, given a set D of documents, to preprocess D so that for any string p and for any positive integer d, all the superstrings of p that are d-left-right maximal can be answered quickly. In this paper, we present an O(n log m) space data structure (in words) which answers queries in O(|p| + o log log m) time, where n is the total length of documents in D, m is the number of documents in D and o is the number of outputs. Our solution improves the previous one by Nishimoto et al. (PSC 2015), which uses an O(n log n) space data structure answering queries in O(|p| + r · log n + o · log2 n) time, where r is the number of right-extensions q of p occurring in at least d documents such that any proper right extension of q occurs in less than d documents.

UR - http://www.scopus.com/inward/record.url?scp=85076353657&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85076353657&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ISAAC.2019.40

DO - 10.4230/LIPIcs.ISAAC.2019.40

M3 - Conference contribution

AN - SCOPUS:85076353657

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 30th International Symposium on Algorithms and Computation, ISAAC 2019

A2 - Lu, Pinyan

A2 - Zhang, Guochuan

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

ER -