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Computing Minimal and Maximal Suffixes of a Substring Revisited

  • Maxim Babenko
  • Paweł Gawrychowski
  • Tomasz Kociumaka
  • Tatiana Starikovskaya
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8486)

Abstract

We revisit the problems of computing the maximal and the minimal non-empty suffixes of a substring of a longer text of length n, introduced by Babenko, Kolesnichenko and Starikovskaya [CPM’13]. For the minimal suffix problem we show that for any 1 ≤ τ ≤ logn there exists a linear-space data structure with \(\mathcal{O}(\tau)\) query time and \(\mathcal{O}(n \log n / \tau)\) preprocessing time. As a sample application, we show that this data structure can be used to compute the Lyndon decomposition of any substring of the text in \(\mathcal{O}(k \tau)\) time, where k is the number of distinct factors in the decomposition. For the maximal suffix problem we give a linear-space structure with \(\mathcal{O}(1)\) query time and \(\mathcal{O}(n)\) preprocessing time, i.e., we manage to achieve both the optimal query and the optimal construction time simultaneously.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Maxim Babenko
    • 1
  • Paweł Gawrychowski
    • 2
  • Tomasz Kociumaka
    • 3
  • Tatiana Starikovskaya
    • 1
  1. 1.National Research University Higher School of Economics (HSE)Russia
  2. 2.Max-Planck-Institut für InformatikGermany
  3. 3.Institute of InformaticsUniversity of WarsawPoland

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