Cover Array String Reconstruction

  • Maxime Crochemore
  • Costas S. Iliopoulos
  • Solon P. Pissis
  • German Tischler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6129)

Abstract

A proper factor u of a string y is a cover of y if every letter of y is within some occurrence of u in y. The concept generalises the notion of periods of a string. An integer array \({\mathit{C}}\) is the minimal-cover (resp. maximal-cover) array of y if \({\mathit{C}}[i]\) is the minimal (resp. maximal) length of covers of \(y[0{\ldotp\ldotp}i]\), or zero if no cover exists.

In this paper, we present a constructive algorithm checking the validity of an array as a minimal-cover or maximal-cover array of some string. When the array is valid, the algorithm produces a string over an unbounded alphabet whose cover array is the input array. All algorithms run in linear time due to an interesting combinatorial property of cover arrays: the sum of important values in a cover array is bounded by twice the length of the string.

Keywords

Veri Rovan 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Maxime Crochemore
    • 1
    • 2
  • Costas S. Iliopoulos
    • 1
    • 3
  • Solon P. Pissis
    • 1
  • German Tischler
    • 1
    • 4
  1. 1.Dept. of Computer ScienceKing’s College LondonLondonUK
  2. 2.Université Paris-EstFrance
  3. 3.Digital Ecosystems & Business Intelligence InstituteCurtin UniversityPerthAustralia
  4. 4.Newton Fellow 

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