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Verifying a Parameterized Border Array in O(n 1.5) Time

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Combinatorial Pattern Matching (CPM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6129))

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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 \(\frac{1}{e} \sum_{k=0}^{\infty} \frac{k^{n}}{k!}\), and hence our algorithm is quite efficient.

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Author information

Authors and Affiliations

  1. Department of Informatics, Kyushu University,  

    Tomohiro I., Hideo Bannai & Masayuki Takeda

  2. Graduate School of Information Science and Electrical Engineering, Kyushu University, 744 Motooka, Nishiku, Fukuoka, 819–0395, Japan

    Shunsuke Inenaga

Authors
  1. Tomohiro I.
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  2. Shunsuke Inenaga
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  3. Hideo Bannai
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  4. Masayuki Takeda
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Johns Hopkins University, Baltimore, MD, USA, and Bar-Ilan University, 52900, Ramat-Gan, Israel

    Amihood Amir

  2. IBM T.J. Watson Research Center, Yorktown Heights, NY, USA

    Laxmi Parida

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© 2010 Springer-Verlag Berlin Heidelberg

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I., T., Inenaga, S., Bannai, H., Takeda, M. (2010). Verifying a Parameterized Border Array in O(n 1.5) Time. In: Amir, A., Parida, L. (eds) Combinatorial Pattern Matching. CPM 2010. Lecture Notes in Computer Science, vol 6129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13509-5_22

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  • DOI: https://doi.org/10.1007/978-3-642-13509-5_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13508-8

  • Online ISBN: 978-3-642-13509-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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