Abstract
A string \(x = uvu\) with both u, v being non-empty is called a gapped repeat with period \(p = |uv|\), and is denoted by pair (x, p). If \(p \le \alpha (|x|-p)\) with \(\alpha > 1\), then (x, p) is called an \(\alpha \) -gapped repeat. An occurrence \([i, i+|x|-1]\) of an \(\alpha \)-gapped repeat (x, p) in a string w is called a maximal \(\alpha \)-gapped repeat of w, if it cannot be extended either to the left or to the right in w with the same period p. Kolpakov et al. (CPM 2014) showed that, given a string of length n over a constant alphabet, all the occurrences of maximal \(\alpha \)-gapped repeats in the string can be computed in \(O(\alpha ^2 n + occ )\) time, where \( occ \) is the number of occurrences. In this paper, we propose a faster \(O(\alpha n + occ )\)-time algorithm to solve this problem, improving the result of Kolpakov et al. by a factor of \(\alpha \).
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Tanimura, Y., Fujishige, Y., I, T., Inenaga, S., Bannai, H., Takeda, M. (2015). A Faster Algorithm for Computing Maximal \(\alpha \)-gapped Repeats in a String. In: Iliopoulos, C., Puglisi, S., Yilmaz, E. (eds) String Processing and Information Retrieval. SPIRE 2015. Lecture Notes in Computer Science(), vol 9309. Springer, Cham. https://doi.org/10.1007/978-3-319-23826-5_13
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DOI: https://doi.org/10.1007/978-3-319-23826-5_13
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