### Abstract

The order preserving pattern matching (OPPM) problem is, given a pattern string p and a text string t, find all substrings of t which have the same relative orders as p. In this paper, we consider two variants of the OPPM problem where a set of text strings is given as a tree or a DAG. We show that the OPPM problem for a single pattern p of length m and a text tree T of size N can be solved in O(m+N) time with O(m) working space if the characters of p are drawn from an integer alphabet of polynomial size. The time complexity becomes O(m log m + N) if the pattern p is over a general ordered alphabet. We then show that the OPPM problem for a single pattern and a text DAG is NP-complete.

Original language | English |
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Title of host publication | String Processing and Information Retrieval - 24th International Symposium, SPIRE 2017, Proceedings |

Editors | Rossano Venturini, Gabriele Fici, Marinella Sciortino |

Publisher | Springer Verlag |

Pages | 271-277 |

Number of pages | 7 |

ISBN (Print) | 9783319674278 |

DOIs | |

Publication status | Published - Jan 1 2017 |

Event | 24th International Symposium on String Processing and Information Retrieval, SPIRE 2017 - Palermo, Italy Duration: Sep 26 2017 → Sep 29 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 | 10508 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 24th International Symposium on String Processing and Information Retrieval, SPIRE 2017 |
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Country | Italy |

City | Palermo |

Period | 9/26/17 → 9/29/17 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*String Processing and Information Retrieval - 24th International Symposium, SPIRE 2017, Proceedings*(pp. 271-277). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10508 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-67428-5_23

**Order preserving pattern matching on trees and DAGs.** / Nakamura, Temma; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

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

*String Processing and Information Retrieval - 24th International Symposium, SPIRE 2017, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10508 LNCS, Springer Verlag, pp. 271-277, 24th International Symposium on String Processing and Information Retrieval, SPIRE 2017, Palermo, Italy, 9/26/17. https://doi.org/10.1007/978-3-319-67428-5_23

}

TY - GEN

T1 - Order preserving pattern matching on trees and DAGs

AU - Nakamura, Temma

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2017/1/1

Y1 - 2017/1/1

N2 - The order preserving pattern matching (OPPM) problem is, given a pattern string p and a text string t, find all substrings of t which have the same relative orders as p. In this paper, we consider two variants of the OPPM problem where a set of text strings is given as a tree or a DAG. We show that the OPPM problem for a single pattern p of length m and a text tree T of size N can be solved in O(m+N) time with O(m) working space if the characters of p are drawn from an integer alphabet of polynomial size. The time complexity becomes O(m log m + N) if the pattern p is over a general ordered alphabet. We then show that the OPPM problem for a single pattern and a text DAG is NP-complete.

AB - The order preserving pattern matching (OPPM) problem is, given a pattern string p and a text string t, find all substrings of t which have the same relative orders as p. In this paper, we consider two variants of the OPPM problem where a set of text strings is given as a tree or a DAG. We show that the OPPM problem for a single pattern p of length m and a text tree T of size N can be solved in O(m+N) time with O(m) working space if the characters of p are drawn from an integer alphabet of polynomial size. The time complexity becomes O(m log m + N) if the pattern p is over a general ordered alphabet. We then show that the OPPM problem for a single pattern and a text DAG is NP-complete.

UR - http://www.scopus.com/inward/record.url?scp=85030168258&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030168258&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-67428-5_23

DO - 10.1007/978-3-319-67428-5_23

M3 - Conference contribution

AN - SCOPUS:85030168258

SN - 9783319674278

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

SP - 271

EP - 277

BT - String Processing and Information Retrieval - 24th International Symposium, SPIRE 2017, Proceedings

A2 - Venturini, Rossano

A2 - Fici, Gabriele

A2 - Sciortino, Marinella

PB - Springer Verlag

ER -