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 ≤ α(|x| − p) with α > 1, then (x, p) is called an α-gapped repeat. An occurrence [i, i+|x|−1] of an α-gapped repeat (x, p) in a string w is called a maximal α-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 α-gapped repeats in the string can be computed in O(α2n+occ) time, where occ is the number of occurrences. In this paper, we propose a faster O(αn + occ)-time algorithm to solve this problem, improving the result of Kolpakov et al. by a factor of α.
CITATION STYLE
Tanimura, Y., Fujishige, Y., I, T., Inenaga, S., Bannai, H., & Takeda, M. (2015). A faster algorithm for computing maximal α-gapped repeats in a string. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9309, pp. 124–136). Springer Verlag. https://doi.org/10.1007/978-3-319-23826-5_13
Mendeley helps you to discover research relevant for your work.