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A Minimal Periods Algorithm with Applications

  • Conference paper
Combinatorial Pattern Matching (CPM 2010)

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

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Abstract

Kosaraju in “Computation of squares in a string” briefly described a linear-time algorithm for computing the minimal squares starting at each position in a word. Using the same construction of suffix trees, we generalize his result and describe in detail how to compute the minimal α power, with a period of length longer than s, starting at each position in a word w for arbitrary exponent α> 1 and integer s ≥ 0. The algorithm runs in O(α|w|)-time for s = 0 and in O(|w|2)-time otherwise. We provide a complete proof of the correctness and computational complexity of the algorithm. The algorithm can be used to detect certain types of pseudo-patterns in words, which was our original goal in studying this generalization.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Middlesex College, The University of Western Ontario, London, Ontario, Canada, N6A 5B7

    Zhi Xu

Authors
  1. Zhi Xu
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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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Xu, Z. (2010). A Minimal Periods Algorithm with Applications. 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_6

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  • DOI: https://doi.org/10.1007/978-3-642-13509-5_6

  • 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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