License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2018.70
URN: urn:nbn:de:0030-drops-100184
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Kociumaka, Tomasz ; Kundu, Ritu ; Mohamed, Manal ; Pissis, Solon P.

Longest Unbordered Factor in Quasilinear Time

LIPIcs-ISAAC-2018-70.pdf (0.6 MB)


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].

BibTeX - Entry

  author =	{Tomasz Kociumaka and Ritu Kundu and Manal Mohamed and Solon P. Pissis},
  title =	{{Longest Unbordered Factor in Quasilinear Time}},
  booktitle =	{29th International Symposium on Algorithms and Computation  (ISAAC 2018)},
  pages =	{70:1--70:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Wen-Lian Hsu and Der-Tsai Lee and Chung-Shou Liao},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-100184},
  doi =		{10.4230/LIPIcs.ISAAC.2018.70},
  annote =	{Keywords: longest unbordered factor, factorisation, period, border, strings}

Keywords: longest unbordered factor, factorisation, period, border, strings
Collection: 29th International Symposium on Algorithms and Computation (ISAAC 2018)
Issue Date: 2018
Date of publication: 06.12.2018

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