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)


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.


Linear Time Word Length Constructive Algorithm Validity Check Algorithm Prune 
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 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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