eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-12-06
70:1
70:13
10.4230/LIPIcs.ISAAC.2018.70
article
Longest Unbordered Factor in Quasilinear Time
Kociumaka, Tomasz
1
https://orcid.org/0000-0002-2477-1702
Kundu, Ritu
2
https://orcid.org/0000-0003-1353-4004
Mohamed, Manal
2
https://orcid.org/0000-0002-1435-5051
Pissis, Solon P.
2
https://orcid.org/0000-0002-1445-1932
Institute of Informatics, University of Warsaw, Warsaw, Poland
Department of Informatics, King’s College London, London, UK
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].
https://drops.dagstuhl.de/storage/00lipics/lipics-vol123-isaac2018/LIPIcs.ISAAC.2018.70/LIPIcs.ISAAC.2018.70.pdf
longest unbordered factor
factorisation
period
border
strings