Longest Unbordered Factor in Quasilinear Time

Authors Tomasz Kociumaka , Ritu Kundu , Manal Mohamed , Solon P. Pissis

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Author Details

Tomasz Kociumaka
  • Institute of Informatics, University of Warsaw, Warsaw, Poland
Ritu Kundu
  • Department of Informatics, King’s College London, London, UK
Manal Mohamed
  • Department of Informatics, King’s College London, London, UK
Solon P. Pissis
  • Department of Informatics, King’s College London, London, UK

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Tomasz Kociumaka, Ritu Kundu, Manal Mohamed, and Solon P. Pissis. Longest Unbordered Factor in Quasilinear Time. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 70:1-70:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


A border u of a word w is a proper factor of w occurring both as a prefix and as a suffix. The maximal unbordered factor of w is the longest factor of w which does not have a border. Here an O(n log n)-time with high probability (or O(n log n log^2 log n)-time deterministic) algorithm to compute the Longest Unbordered Factor Array of w for general alphabets is presented, where n is the length of w. This array specifies the length of the maximal unbordered factor starting at each position of w. This is a major improvement on the running time of the currently best worst-case algorithm working in O(n^{1.5}) time for integer alphabets [Gawrychowski et al., 2015].

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
  • longest unbordered factor
  • factorisation
  • period
  • border
  • strings


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