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].
@InProceedings{kociumaka_et_al:LIPIcs.ISAAC.2018.70, author = {Kociumaka, Tomasz and Kundu, Ritu and Mohamed, Manal and Pissis, Solon P.}, 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 = {Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.70}, 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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