Shortest unique palindromic substring queries in optimal time

Yuto Nakashima; Hiroe Inoue; Takuya Mieno; Shunsuke Inenaga; Hideo Bannai; Masayuki Takeda

doi:10.1007/978-3-319-78825-8_32

Shortest unique palindromic substring queries in optimal time

Yuto Nakashima, Hiroe Inoue, Takuya Mieno, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda

Mathematical Informatics

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

Abstract

palindrome is a string that reads the same forward and backward. A palindromic substring P of a string S is called a shortest unique palindromic substring (SUPS) for an interval [s, t] in S, if P occurs exactly once in S, this occurrence of P contains interval [s, t], and every palindromic substring of S which contains interval [s, t] and is shorter than P occurs at least twice in S. The SUPS problem is, given a string S, to preprocess S so that for any subsequent query interval [s, t] all the SUPSs for interval [s, t] can be answered quickly. We present an optimal solution to this problem. Namely, we show how to preprocess a given string S of length n in O(n) time and space so that all SUPSs for any subsequent query interval can be answered in O(α + 1) time, where α is the number of outputs.

Original language	English
Title of host publication	Combinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers
Editors	William F. Smyth, Ljiljana Brankovic, Joe Ryan
Publisher	Springer Verlag
Pages	397-408
Number of pages	12
ISBN (Print)	9783319788241
DOIs	https://doi.org/10.1007/978-3-319-78825-8_32
Publication status	Published - 2018
Event	28th International Workshop on Combinational Algorithms, IWOCA 2017 - Newcastle, NSW, Australia Duration: Jul 17 2017 → Jul 21 2017

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10765 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	28th International Workshop on Combinational Algorithms, IWOCA 2017
Country/Territory	Australia
City	Newcastle, NSW
Period	7/17/17 → 7/21/17

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-319-78825-8_32

Cite this

Nakashima, Y., Inoue, H., Mieno, T., Inenaga, S., Bannai, H., & Takeda, M. (2018). Shortest unique palindromic substring queries in optimal time. In W. F. Smyth, L. Brankovic, & J. Ryan (Eds.), Combinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers (pp. 397-408). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10765 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-78825-8_32

Shortest unique palindromic substring queries in optimal time. / Nakashima, Yuto; Inoue, Hiroe; Mieno, Takuya et al.
Combinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers. ed. / William F. Smyth; Ljiljana Brankovic; Joe Ryan. Springer Verlag, 2018. p. 397-408 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10765 LNCS).

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

Nakashima, Y, Inoue, H, Mieno, T, Inenaga, S, Bannai, H & Takeda, M 2018, Shortest unique palindromic substring queries in optimal time. in WF Smyth, L Brankovic & J Ryan (eds), Combinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10765 LNCS, Springer Verlag, pp. 397-408, 28th International Workshop on Combinational Algorithms, IWOCA 2017, Newcastle, NSW, Australia, 7/17/17. https://doi.org/10.1007/978-3-319-78825-8_32

Nakashima Y, Inoue H, Mieno T, Inenaga S, Bannai H, Takeda M. Shortest unique palindromic substring queries in optimal time. In Smyth WF, Brankovic L, Ryan J, editors, Combinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers. Springer Verlag. 2018. p. 397-408. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-78825-8_32

Nakashima, Yuto ; Inoue, Hiroe ; Mieno, Takuya et al. / Shortest unique palindromic substring queries in optimal time. Combinatorial Algorithms - 28th International Workshop, IWOCA 2017, Revised Selected Papers. editor / William F. Smyth ; Ljiljana Brankovic ; Joe Ryan. Springer Verlag, 2018. pp. 397-408 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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author = "Yuto Nakashima and Hiroe Inoue and Takuya Mieno and Shunsuke Inenaga and Hideo Bannai and Masayuki Takeda",

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AU - Bannai, Hideo

AU - Takeda, Masayuki

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AB - palindrome is a string that reads the same forward and backward. A palindromic substring P of a string S is called a shortest unique palindromic substring (SUPS) for an interval [s, t] in S, if P occurs exactly once in S, this occurrence of P contains interval [s, t], and every palindromic substring of S which contains interval [s, t] and is shorter than P occurs at least twice in S. The SUPS problem is, given a string S, to preprocess S so that for any subsequent query interval [s, t] all the SUPSs for interval [s, t] can be answered quickly. We present an optimal solution to this problem. Namely, we show how to preprocess a given string S of length n in O(n) time and space so that all SUPSs for any subsequent query interval can be answered in O(α + 1) time, where α is the number of outputs.

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Shortest unique palindromic substring queries in optimal time

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