### Abstract

Let and be disjoint alphabets of respective size and. Two strings over of equal length are said to parameterized match (p-match) if there is a bijection such that (1) f is identity on and (2) f maps the characters of one string to those of the other string so that the two strings become identical. We consider the p-matching problem on a (reversed) trie and a string pattern P such that every path that p-matches P has to be reported. Let N be the size of the given trie. In this paper, we propose the parameterized position heap for that occupies O(N) space and supports p-matching queries in time, where m is the length of a query pattern P and is the number of paths in to report. We also present an algorithm which constructs the parameterized position heap for a given trie in time and working space.

Original language | English |
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Title of host publication | Algorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings |

Editors | Pinar Heggernes |

Publisher | Springer Verlag |

Pages | 237-248 |

Number of pages | 12 |

ISBN (Print) | 9783030174019 |

DOIs | |

Publication status | Published - Jan 1 2019 |

Event | 11th International Conference on Algorithms and Complexity, CIAC 2019 - Rome, Italy Duration: May 27 2019 → May 29 2019 |

### 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 | 11485 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 11th International Conference on Algorithms and Complexity, CIAC 2019 |
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Country | Italy |

City | Rome |

Period | 5/27/19 → 5/29/19 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings*(pp. 237-248). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11485 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-17402-6_20

**The Parameterized Position Heap of a Trie.** / Fujisato, Noriki; Nakashima, Yuto; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

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

*Algorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11485 LNCS, Springer Verlag, pp. 237-248, 11th International Conference on Algorithms and Complexity, CIAC 2019, Rome, Italy, 5/27/19. https://doi.org/10.1007/978-3-030-17402-6_20

}

TY - GEN

T1 - The Parameterized Position Heap of a Trie

AU - Fujisato, Noriki

AU - Nakashima, Yuto

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Let and be disjoint alphabets of respective size and. Two strings over of equal length are said to parameterized match (p-match) if there is a bijection such that (1) f is identity on and (2) f maps the characters of one string to those of the other string so that the two strings become identical. We consider the p-matching problem on a (reversed) trie and a string pattern P such that every path that p-matches P has to be reported. Let N be the size of the given trie. In this paper, we propose the parameterized position heap for that occupies O(N) space and supports p-matching queries in time, where m is the length of a query pattern P and is the number of paths in to report. We also present an algorithm which constructs the parameterized position heap for a given trie in time and working space.

AB - Let and be disjoint alphabets of respective size and. Two strings over of equal length are said to parameterized match (p-match) if there is a bijection such that (1) f is identity on and (2) f maps the characters of one string to those of the other string so that the two strings become identical. We consider the p-matching problem on a (reversed) trie and a string pattern P such that every path that p-matches P has to be reported. Let N be the size of the given trie. In this paper, we propose the parameterized position heap for that occupies O(N) space and supports p-matching queries in time, where m is the length of a query pattern P and is the number of paths in to report. We also present an algorithm which constructs the parameterized position heap for a given trie in time and working space.

UR - http://www.scopus.com/inward/record.url?scp=85066911091&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066911091&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-17402-6_20

DO - 10.1007/978-3-030-17402-6_20

M3 - Conference contribution

AN - SCOPUS:85066911091

SN - 9783030174019

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

SP - 237

EP - 248

BT - Algorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings

A2 - Heggernes, Pinar

PB - Springer Verlag

ER -