Kociumaka, Tomasz ;
Kundu, Ritu ;
Mohamed, Manal ;
Pissis, Solon P.
Longest Unbordered Factor in Quasilinear Time
Abstract
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
@InProceedings{kociumaka_et_al:LIPIcs:2018:10018,
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 = {http://drops.dagstuhl.de/opus/volltexte/2018/10018},
URN = {urn:nbn:de:0030-drops-100184},
doi = {10.4230/LIPIcs.ISAAC.2018.70},
annote = {Keywords: longest unbordered factor, factorisation, period, border, strings}
}
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Keywords: |
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longest unbordered factor, factorisation, period, border, strings |
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Seminar: |
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29th International Symposium on Algorithms and Computation (ISAAC 2018)
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Issue date: |
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2018 |
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Date of publication: |
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2018 |
2018
