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Reversing Longest Previous Factor Tables is Hard

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Algorithms and Data Structures (WADS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6844))

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Abstract

The Longest Previous Factor (LPF) table of a string s of length n is a table of size n whose i th element indicates the length of the longest substring of s starting from position i that has appeared previously in s. LPF tables facilitate the computing of the Lempel-Ziv factorization of strings [21,22] which plays an important role in text compression. An open question from Clément, Crochemore and Rindone [4] asked whether the following problem (which we call the reverse LPF problem) can be solved efficiently: Given a table W, decide whether it is the LPF table of some string, and find such a string if so.

In this paper, we address this open question by proving that the reverse LPF problem is NP-hard. Thus, there is no polynomial time algorithm for solving it unless P = NP. Complementing with this general hardness result, we also design a linear-time online algorithm for the reverse LPF problem over input tables whose elements are all 0 or 1.

This work was supported in part by the National Basic Research Program of China Grant 2007CB807900, 2007CB807901, and the National Natural Science Foundation of China Grant 61033001, 61061130540, 61073174.

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Authors and Affiliations

  1. IInstitute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China

    Jing He, Hongyu Liang & Guang Yang

Authors
  1. Jing He
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  2. Hongyu Liang
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  3. Guang Yang
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Editor information

Editors and Affiliations

  1. School of Computer Science, Parallel Computing and Bioinformatics Laboratory, Carleton University, VISM Building, Room 6210, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Frank Dehne

  2. Department of Computer Science and Engineering, Polytechnic Institute of New York University, 5 MetroTech Center, 11201, New York, NY, USA

    John Iacono

  3. School of Computer Science, Herzberg Laboratories, Carleton University, Herzberg Building, Room 5350, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Jörg-Rüdiger Sack

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He, J., Liang, H., Yang, G. (2011). Reversing Longest Previous Factor Tables is Hard. In: Dehne, F., Iacono, J., Sack, JR. (eds) Algorithms and Data Structures. WADS 2011. Lecture Notes in Computer Science, vol 6844. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22300-6_41

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  • DOI: https://doi.org/10.1007/978-3-642-22300-6_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22299-3

  • Online ISBN: 978-3-642-22300-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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