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

  • Golnaz Badkobeh
  • Maxime Crochemore
  • Chalita Toopsuwan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Golnaz Badkobeh
    • 1
  • Maxime Crochemore
    • 1
    • 2
  • Chalita Toopsuwan
    • 1
  1. 1.King’s College LondonUK
  2. 2.Université Paris-EstFrance

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