TY - GEN
T1 - Finding gapped palindromes online
AU - Fujishige, Yuta
AU - Nakamura, Michitaro
AU - Inenaga, Shunsuke
AU - Bannai, Hideo
AU - Takeda, Masayuki
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.
PY - 2016
Y1 - 2016
N2 - A string s is said to be a gapped palindrome iff s = xyxRfor some strings x, y such that |x| ≥ 1, |y| ≥ 2, and xR denotes the reverse image of x.In this paper we consider two kinds of gapped palindromes, and present efficient online algorithms to compute these gapped palindromes occurring in a string.First, we show an online algorithm to find all maximal g-gapped palindromes with fixed gap length g ≥ 2 in a string of length n in O(n log σ) time and O(n) space, where σ is the alphabet size.Second, we show an online algorithm to find all maximal lengthconstrained gapped palindromes with arm length at least A ≥ 1 and gap length in range [gmin, gmax] in O (formula presented) time and O(n) space.We also show that if A is a constant, then there exists a string of length n which contains Ω(n(gmax− gmin)) maximal LCGPs, which implies we cannot hope for a significant speed-up in the worst case.
AB - A string s is said to be a gapped palindrome iff s = xyxRfor some strings x, y such that |x| ≥ 1, |y| ≥ 2, and xR denotes the reverse image of x.In this paper we consider two kinds of gapped palindromes, and present efficient online algorithms to compute these gapped palindromes occurring in a string.First, we show an online algorithm to find all maximal g-gapped palindromes with fixed gap length g ≥ 2 in a string of length n in O(n log σ) time and O(n) space, where σ is the alphabet size.Second, we show an online algorithm to find all maximal lengthconstrained gapped palindromes with arm length at least A ≥ 1 and gap length in range [gmin, gmax] in O (formula presented) time and O(n) space.We also show that if A is a constant, then there exists a string of length n which contains Ω(n(gmax− gmin)) maximal LCGPs, which implies we cannot hope for a significant speed-up in the worst case.
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U2 - 10.1007/978-3-319-44543-4_15
DO - 10.1007/978-3-319-44543-4_15
M3 - Conference contribution
AN - SCOPUS:84984908030
SN - 9783319445427
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 191
EP - 202
BT - Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings
A2 - Mäkinen, Veli
A2 - Puglisi, Simon J.
A2 - Salmela, Leena
PB - Springer Verlag
T2 - 27th International Workshop on Combinatorial Algorithms, IWOCA 2016
Y2 - 17 August 2016 through 19 August 2016
ER -