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Internal Longest Palindrome Queries in Optimal Time

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WALCOM: Algorithms and Computation (WALCOM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13973))

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Abstract

Palindromes are strings that read the same forward and backward. Problems of computing palindromic structures in strings have been studied for many years with a motivation of their application to biology. The longest palindrome problem is one of the most important and classical problems regarding palindromic structures, that is, to compute the longest palindrome appearing in a string T of length n. The problem can be solved in \(\mathcal {O}(n)\) time by the famous algorithm of Manacher [Journal of the ACM, 1975]. In this paper, we consider the problem in the internal model. The internal longest palindrome query is, given a substring T[i..j] of T as a query, to compute the longest palindrome appearing in T[i..j]. The best known data structure for this problem is the one proposed by Amir et al. [Algorithmica, 2020], which can answer any query in \(\mathcal {O}(\log n)\) time. In this paper, we propose a linear-size data structure that can answer any internal longest palindrome query in constant time. Also, given the input string T, our data structure can be constructed in \(\mathcal {O}(n)\) time.

Partially supported by JSPS KAKENHI Grant Numbers JP20H05964.

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Author information

Authors and Affiliations

  1. Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan

    Kazuki Mitani

  2. Department of Computer and Network Engineering, University of Electro-Communications, Chofu, Japan

    Takuya Mieno

  3. Faculty of Information Science and Technology, Hokkaido University, Sapporo, Japan

    Kazuhisa Seto & Takashi Horiyama

Authors
  1. Kazuki Mitani
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  2. Takuya Mieno
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  3. Kazuhisa Seto
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  4. Takashi Horiyama
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Correspondence to Takuya Mieno .

Editor information

Editors and Affiliations

  1. National Yang Ming Chiao Tung University, Hsinchu, Taiwan

    Chun-Cheng Lin

  2. National Yang Ming Chiao Tung University, Hsinchu, Taiwan

    Bertrand M. T. Lin

  3. University of Perugia, Perugia, Italy

    Giuseppe Liotta

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Mitani, K., Mieno, T., Seto, K., Horiyama, T. (2023). Internal Longest Palindrome Queries in Optimal Time. In: Lin, CC., Lin, B.M.T., Liotta, G. (eds) WALCOM: Algorithms and Computation. WALCOM 2023. Lecture Notes in Computer Science, vol 13973. Springer, Cham. https://doi.org/10.1007/978-3-031-27051-2_12

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  • DOI: https://doi.org/10.1007/978-3-031-27051-2_12

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