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Finding Ambiguous Patterns on Grammar Compressed String

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New Frontiers in Artificial Intelligence (JSAI-isAI 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9067))

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Abstract

Given a grammar compressed string S, a pattern P, and \(d\ge 0\), we consider the problem of finding all occurrences of \(P'\) in S such that \(d(P,P')\le d\) with respect to Hamming distance. We propose an algorithm for this problem in \(O(\lg \lg n \lg ^* N(m+d\ occ_d \lg \frac{m}{d}\lg N))\) time, where \(N=|S|\), \(m=|P|\), n is the number of variables in the grammar compression, and \(occ_d\) is the frequency of an evidence of a substring of P. We implement this algorithm and compare with a naive filtering on the grammar compression.

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Notes

  1. 1.

    In practical sense, \(\lg ^*N\) is a constant for sufficiently large N.

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Authors and Affiliations

  1. Department of Artificial Intelligence, Kyushu Institute of Technology, Kawazu 680-4, Iizuka, 820, Japan

    Koji Maeda, Yoshimasa Takabatake & Hiroshi Sakamoto

  2. PRESTO, JST, Tokyo, Japan

    Yasuo Tabei

Authors
  1. Koji Maeda
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  2. Yoshimasa Takabatake
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  3. Yasuo Tabei
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  4. Hiroshi Sakamoto
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Corresponding author

Correspondence to Hiroshi Sakamoto .

Editor information

Editors and Affiliations

  1. Tokyo Institute of Technology, Tokyo, Japan

    Tsuyoshi Murata

  2. Ochanomizu University, Tokyo, Japan

    Koji Mineshima

  3. Department Information Science, Faculty of Science, Ochanomizu University , Tokyo, Japan

    Daisuke Bekki

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Maeda, K., Takabatake, Y., Tabei, Y., Sakamoto, H. (2015). Finding Ambiguous Patterns on Grammar Compressed String. In: Murata, T., Mineshima, K., Bekki, D. (eds) New Frontiers in Artificial Intelligence. JSAI-isAI 2014. Lecture Notes in Computer Science(), vol 9067. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48119-6_25

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  • DOI: https://doi.org/10.1007/978-3-662-48119-6_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48118-9

  • Online ISBN: 978-3-662-48119-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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