Efficient Algorithms for Shortest Partial Seeds in Words

  • Tomasz Kociumaka
  • Solon P. Pissis
  • Jakub Radoszewski
  • Wojciech Rytter
  • Tomasz Waleń
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8486)

Abstract

A factor u of a word w is a cover of w if every position in w lies within some occurrence of u in w. A factor u is a seed of w if it is a cover of a superstring of w. Covers and seeds extend the classical notions of periodicity. We introduce a new notion of α-partial seed, that is, a factor covering as a seed at least α positions in a given word. We use the Cover Suffix Tree, introduced recently in the context of α-partial covers (Kociumaka et al, CPM 2013); an \(\mathcal{O}(n\log n)\)-time algorithm constructing such a tree is known. However it appears that partial seeds are more complicated than partial covers—our algorithms require algebraic manipulations of special functions related to edges of the modified Cover Suffix Tree and the border array. We present an algorithm for computing shortest α-partial seeds that works in \(\mathcal{O}(n)\) time if the Cover Suffix Tree is already given.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Tomasz Kociumaka
    • 1
  • Solon P. Pissis
    • 2
  • Jakub Radoszewski
    • 1
  • Wojciech Rytter
    • 1
    • 3
  • Tomasz Waleń
    • 1
  1. 1.Faculty of Mathematics, Informatics and MechanicsUniversity of WarsawWarsawPoland
  2. 2.Department of InformaticsKing’s College LondonLondonUK
  3. 3.Faculty of Mathematics and Computer ScienceCopernicus UniversityToruńPoland

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