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Order Preserving Pattern Matching on Trees and DAGs

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String Processing and Information Retrieval (SPIRE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10508))

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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.

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Notes

  1. 1.

    Simon [14] proposed an O(m)-space Morris-Pratt automaton for exact pattern matching, however, it is unclear if this can be extended to PPM or OPPM.

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Authors and Affiliations

  1. Department of Informatics, Kyushu University, Fukuoka, Japan

    Temma Nakamura, Shunsuke Inenaga, Hideo Bannai & Masayuki Takeda

Authors
  1. Temma Nakamura
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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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Corresponding author

Correspondence to Temma Nakamura .

Editor information

Editors and Affiliations

  1. Università di Palermo, Palermo, Italy

    Gabriele Fici

  2. Università di Palermo, Palermo, Italy

    Marinella Sciortino

  3. Università di Pisa, Pisa, Italy

    Rossano Venturini

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Nakamura, T., Inenaga, S., Bannai, H., Takeda, M. (2017). Order Preserving Pattern Matching on Trees and DAGs. In: Fici, G., Sciortino, M., Venturini, R. (eds) String Processing and Information Retrieval. SPIRE 2017. Lecture Notes in Computer Science(), vol 10508. Springer, Cham. https://doi.org/10.1007/978-3-319-67428-5_23

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  • DOI: https://doi.org/10.1007/978-3-319-67428-5_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67427-8

  • Online ISBN: 978-3-319-67428-5

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