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Computing the Maximal-Exponent Repeats of an Overlap-Free String in Linear Time

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7608)

Abstract

The exponent of a string is the quotient of the string’s length over the string’s smallest period. The exponent and the period of a string can be computed in time proportional to the string’s length. We design an algorithm to compute the maximal exponent of factors of an overlap-free string. Our algorithm runs in linear-time on a fixed-size alphabet, while a naive solution of the question would run in cubic time. The solution for non overlap-free strings derives from algorithms to compute all maximal repetitions, also called runs, occurring in the string. We show there is a linear number of maximal-exponent repeats in an overlap-free string. The algorithm can locate all of them in linear time.

Keywords

  • Linear Time
  • String Length
  • Maximal Repetition
  • Input String
  • Alphabet Size

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Badkobeh, G., Crochemore, M., Toopsuwan, C. (2012). Computing the Maximal-Exponent Repeats of an Overlap-Free String in Linear Time. In: Calderón-Benavides, L., González-Caro, C., Chávez, E., Ziviani, N. (eds) String Processing and Information Retrieval. SPIRE 2012. Lecture Notes in Computer Science, vol 7608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34109-0_8

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  • DOI: https://doi.org/10.1007/978-3-642-34109-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34108-3

  • Online ISBN: 978-3-642-34109-0

  • eBook Packages: Computer ScienceComputer Science (R0)