### Abstract

The parameterized pattern matching problem is to check if there exists a renaming bijection on the alphabet with which a given pattern can be transformed into a substring of a given text. A parameterized border array (p-border array) is a parameterized version of a standard border array, and we can efficiently solve the parameterized pattern matching problem using p-border arrays. In this paper we present an O(n^{1.5})-time O(n)-space algorithm to verify if a given integer array of length n is a valid p-border array for an unbounded alphabet. The best previously known solution takes time proportional to the n-th Bell number 1/e Σ_{k=0} ^{∞} k^{n}/k! , and hence our algorithm is quite efficient.

Original language | English |
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Title of host publication | Combinatorial Pattern Matching - 21st Annual Symposium, CPM 2010, Proceedings |

Publisher | Springer Verlag |

Pages | 238-250 |

Number of pages | 13 |

ISBN (Print) | 3642135080, 9783642135088 |

DOIs | |

Publication status | Published - Jan 1 2010 |

### 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 | 6129 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Combinatorial Pattern Matching - 21st Annual Symposium, CPM 2010, Proceedings*(pp. 238-250). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6129). Springer Verlag. https://doi.org/10.1007/978-3-642-13509-5_22