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On the Computation of Longest Previous Non-overlapping Factors

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String Processing and Information Retrieval (SPIRE 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11811))

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Abstract

The f-factorization of a string is similar to the well-known Lempel-Ziv (LZ) factorization, but differs from it in that the factors must be non-overlapping. There are two linear time algorithms that compute the f-factorization. Both of them compute the array of longest previous non-overlapping factors (\(\mathsf {LPnF}\)-array), from which the f-factorization can easily be derived. In this paper, we present a simple algorithm that computes the \(\mathsf {LPnF}\)-array from the \(\mathsf {LPF}\)-array and an array \(\mathsf {prevOcc}\) that stores positions of previous occurrences of LZ-factors. The algorithm has a linear worst-case time complexity if \(\mathsf {prevOcc}\) contains leftmost positions. Moreover, we provide an algorithm that computes the f-factorization directly. Experiments show that our first method (combined with efficient \(\mathsf {LPF}\)-algorithms) is the fastest and our second method is the most space efficient way to compute the f-factorization.

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Notes

  1. 1.

    In the implementation, T is terminated by a special (EOF) symbol.

  2. 2.

    https://www.uni-ulm.de/in/theo/research/seqana/.

  3. 3.

    http://pizzachili.dcc.uchile.cl.

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Authors and Affiliations

  1. Institute of Theoretical Computer Science, Ulm University, 89069, Ulm, Germany

    Enno Ohlebusch & Pascal Weber

Authors
  1. Enno Ohlebusch
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  2. Pascal Weber
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Correspondence to Enno Ohlebusch .

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Editors and Affiliations

  1. University of A Coruña, A Coruña, Spain

    Nieves R. Brisaboa

  2. University of Helsinki, Helsinki, Finland

    Simon J. Puglisi

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Ohlebusch, E., Weber, P. (2019). On the Computation of Longest Previous Non-overlapping Factors. In: Brisaboa, N., Puglisi, S. (eds) String Processing and Information Retrieval. SPIRE 2019. Lecture Notes in Computer Science(), vol 11811. Springer, Cham. https://doi.org/10.1007/978-3-030-32686-9_26

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  • DOI: https://doi.org/10.1007/978-3-030-32686-9_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-32685-2

  • Online ISBN: 978-3-030-32686-9

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