Abstract
A string is closed if it has length 1 or has a nonempty border without internal occurrences. In this paper we introduce the definition of a maximal closed substring (MCS), which is an occurrence of a closed substring that cannot be extended to the left nor to the right into a longer closed substring. MCSs with exponent at least 2 are commonly called runs; those with exponent smaller than 2, instead, are particular cases of maximal gapped repeats. We show that a string of length n contains \(\mathcal O(n^{1.5})\) MCSs. We also provide an output-sensitive algorithm that, given a string of length n over a constant-size alphabet, locates all m MCSs the string contains in \(\mathcal O(n\log n + m)\) time.
Gabriele Fici is partly supported by MIUR project PRIN 2017 ADASCOML – 2017K7XPAN. Simon J. Puglisi is partly supported by the Academy of Finland, through grant 339070.
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Badkobeh, G., De Luca, A., Fici, G., Puglisi, S.J. (2022). Maximal Closed Substrings. In: Arroyuelo, D., Poblete, B. (eds) String Processing and Information Retrieval. SPIRE 2022. Lecture Notes in Computer Science, vol 13617. Springer, Cham. https://doi.org/10.1007/978-3-031-20643-6_2
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