Compressed string-matching in standard Sturmian words

  • Authors:

  • Pawe Baturo;Wojciech Rytter

  • Affiliations:

  • Faculty of Mathematics and Informatics, Copernicus University, Torun;Institute of Informatics, Warsaw University, Warsaw, Poland and Faculty of Mathematics and Informatics, Copernicus University, Torun

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2009

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Abstract

We present a simple algorithm which for an explicitly given input string pat (a pattern) and a standard Sturmian word x described by the recurrences of size n computes, in time O(|pat|+n), the set of all occurrences of pat in x as a single arithmetic progression (modulo the length of x). The algorithm can be extended to the case when some letters of the pattern are replaced by a don't care symbol. In this case the set of all occurrences does not need to be a single arithmetic progression and our algorithm produces linearly many (with respect to the size of pat) arithmetic progressions. It is an example of fast computations for the input given in a compressed form. In our special case the length of the standard Sturmian word x is usually exponential with respect to the size of the input.