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Efficient Seeds Computation Revisited

  • Michalis Christou
  • Maxime Crochemore
  • Costas S. Iliopoulos
  • Marcin Kubica
  • Solon P. Pissis
  • Jakub Radoszewski
  • Wojciech Rytter
  • Bartosz Szreder
  • Tomasz Waleń
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6661)

Abstract

The notion of the cover is a generalization of a period of a string, and there are linear time algorithms for finding the shortest cover. The seed is a more complicated generalization of periodicity, it is a cover of a superstring of a given string, and the shortest seed problem is of much higher algorithmic difficulty. The problem is not well understood, no linear time algorithm is known. In the paper we give linear time algorithms for some of its versions — computing shortest left-seed array, longest left-seed array and checking for seeds of a given length. The algorithm for the last problem is used to compute the seed array of a string (i.e., the shortest seeds for all the prefixes of the string) in O(n 2) time. We describe also a simpler alternative algorithm computing efficiently the shortest seeds. As a by-product we obtain an O(nlog(n/m)) time algorithm checking if the shortest seed has length at least m and finding the corresponding seed. We also correct some important details missing in the previously known shortest-seed algorithm (Iliopoulos et al., 1996).

Keywords

Linear Time Time Algorithm Period Array Linear Time Algorithm Cover Array 
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 2011

Authors and Affiliations

  • Michalis Christou
    • 1
  • Maxime Crochemore
    • 1
    • 3
  • Costas S. Iliopoulos
    • 1
    • 4
  • Marcin Kubica
    • 2
  • Solon P. Pissis
    • 1
  • Jakub Radoszewski
    • 2
  • Wojciech Rytter
    • 2
    • 5
  • Bartosz Szreder
    • 2
  • Tomasz Waleń
    • 2
  1. 1.Dept. of InformaticsKing’s College LondonLondonUK
  2. 2.Dept. of Mathematics, Computer Science and MechanicsUniversity of WarsawWarsawPoland
  3. 3.Université Paris-EstFrance
  4. 4.Digital Ecosystems & Business Intelligence InstituteCurtin University of TechnologyPerthAustralia
  5. 5.Dept. of Math. and InformaticsCopernicus UniversityToruńPoland

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