TY - GEN

T1 - A faster algorithm for computing maximal α-gapped repeats in a string

AU - Tanimura, Yuka

AU - Fujishige, Yuta

AU - I, Tomohiro

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84944682942&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84944682942&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-23826-5_13

DO - 10.1007/978-3-319-23826-5_13

M3 - Conference contribution

AN - SCOPUS:84944682942

SN - 9783319238258

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 124

EP - 136

BT - String Processing and Information Retrieval - 22nd International Symposium, SPIRE 2015, Proceedings

A2 - Puglisi, Simon J.

A2 - Iliopoulos, Costas S.

A2 - Yilmaz, Emine

PB - Springer Verlag

T2 - 22nd International Symposium on String Processing and Information Retrieval, SPIRE 2015

Y2 - 1 September 2015 through 4 September 2015

ER -