Finding gapped palindromes online

Yuta Fujishige; Michitaro Nakamura; Shunsuke Inenaga; Hideo Bannai; Masayuki Takeda

doi:10.1007/978-3-319-44543-4_15

Finding gapped palindromes online

Yuta Fujishige, Michitaro Nakamura, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda

Mathematical Informatics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 Citations (Scopus)

Abstract

A string s is said to be a gapped palindrome iff s = xyx^Rfor 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 [g_min, g_max] 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(g_max− g_min)) maximal LCGPs, which implies we cannot hope for a significant speed-up in the worst case.

Original language	English
Title of host publication	Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings
Editors	Veli Mäkinen, Simon J. Puglisi, Leena Salmela
Publisher	Springer Verlag
Pages	191-202
Number of pages	12
ISBN (Print)	9783319445427
DOIs	https://doi.org/10.1007/978-3-319-44543-4_15
Publication status	Published - 2016
Event	27th International Workshop on Combinatorial Algorithms, IWOCA 2016 - Helsinki, Finland Duration: Aug 17 2016 → Aug 19 2016

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9843 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	27th International Workshop on Combinatorial Algorithms, IWOCA 2016
Country/Territory	Finland
City	Helsinki
Period	8/17/16 → 8/19/16

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-319-44543-4_15

Cite this

Fujishige, Y., Nakamura, M., Inenaga, S., Bannai, H., & Takeda, M. (2016). Finding gapped palindromes online. In V. Mäkinen, S. J. Puglisi, & L. Salmela (Eds.), Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings (pp. 191-202). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9843 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-44543-4_15

Finding gapped palindromes online. / Fujishige, Yuta; Nakamura, Michitaro; Inenaga, Shunsuke et al.

Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings. ed. / Veli Mäkinen; Simon J. Puglisi; Leena Salmela. Springer Verlag, 2016. p. 191-202 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9843 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Fujishige, Y, Nakamura, M, Inenaga, S, Bannai, H & Takeda, M 2016, Finding gapped palindromes online. in V Mäkinen, SJ Puglisi & L Salmela (eds), Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9843 LNCS, Springer Verlag, pp. 191-202, 27th International Workshop on Combinatorial Algorithms, IWOCA 2016, Helsinki, Finland, 8/17/16. https://doi.org/10.1007/978-3-319-44543-4_15

Fujishige Y, Nakamura M, Inenaga S, Bannai H, Takeda M. Finding gapped palindromes online. In Mäkinen V, Puglisi SJ, Salmela L, editors, Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings. Springer Verlag. 2016. p. 191-202. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-44543-4_15

Fujishige, Yuta ; Nakamura, Michitaro ; Inenaga, Shunsuke et al. / Finding gapped palindromes online. Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings. editor / Veli Mäkinen ; Simon J. Puglisi ; Leena Salmela. Springer Verlag, 2016. pp. 191-202 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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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Finding gapped palindromes online

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