On the Right-Seed Array of a String

  • Michalis Christou
  • Maxime Crochemore
  • Ondrej Guth
  • Costas S. Iliopoulos
  • Solon P. Pissis
Conference paper

DOI: 10.1007/978-3-642-22685-4_43

Volume 6842 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Christou M., Crochemore M., Guth O., Iliopoulos C.S., Pissis S.P. (2011) On the Right-Seed Array of a String. In: Fu B., Du DZ. (eds) Computing and Combinatorics. COCOON 2011. Lecture Notes in Computer Science, vol 6842. Springer, Berlin, Heidelberg

Abstract

We consider the problem of finding the repetitive structure of a given fixed string y. A factor u of y is a cover of y, if every letter of y falls within some occurrence of u in y. A factor v of y is a seed of y, if it is a cover of a superstring of y. There exist linear-time algorithms for solving the minimal cover problem. The minimal seed problem is of much higher algorithmic difficulty, and no linear-time algorithm is known. In this article, we solve one of its variants – computing the minimal and maximal right-seed array of a given string. A right seed of y is the shortest suffix of y that it is a cover of a superstring of y. An integer array RS is the minimal right-seed (resp. maximal right-seed) array of y, if RS[i] is the minimal (resp. maximal) length of right seeds of \(y[0\mathinner{\ldotp\ldotp} i]\). We present an \(\ensuremath{\mathcal{O}}(n\log n)\) time algorithm that computes the minimal right-seed array of a given string, and a linear-time solution to compute the maximal right-seed array by detecting border-free prefixes of the given string.

Keywords

algorithms on strings periodicity covers seeds 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Michalis Christou
    • 1
  • Maxime Crochemore
    • 1
    • 2
  • Ondrej Guth
    • 4
  • Costas S. Iliopoulos
    • 1
    • 3
  • Solon P. Pissis
    • 1
  1. 1.Dept. of InformaticsKing’s College LondonLondonUK
  2. 2.Université Paris-EstFrance
  3. 3.Digital Ecosystems & Business Intelligence InstituteCurtin UniversityPerthAustralia
  4. 4.Dept. of Theoretical Computer Science, Faculty of Information TechnologyCzech Technical University in Prague