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Faster Queries for Longest Substring Palindrome After Block Edit

Authors Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai , Masayuki Takeda

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Author Details

Mitsuru Funakoshi
  • Department of Informatics, Kyushu University, Japan
Yuto Nakashima
  • Department of Informatics, Kyushu University, Japan
Shunsuke Inenaga
  • Department of Informatics, Kyushu University, Japan
Hideo Bannai
  • Department of Informatics, Kyushu University, Japan
Masayuki Takeda
  • Department of Informatics, Kyushu University, Japan

Funding

  • Nakashima, Yuto: Supported by JSPS KAKENHI Grant Number JP18K18002.
  • Inenaga, Shunsuke: Supported by JSPS KAKENHI Grant Number JP17H01697.
  • Bannai, Hideo: Supported by JSPS KAKENHI Grant Number JP16H02783.
  • Takeda, Masayuki: Supported by JSPS KAKENHI Grant Number JP18H04098.

Cite AsGet BibTex

Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Faster Queries for Longest Substring Palindrome After Block Edit. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 27:1-27:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.CPM.2019.27

Abstract

Palindromes are important objects in strings which have been extensively studied from combinatorial, algorithmic, and bioinformatics points of views. Manacher [J. ACM 1975] proposed a seminal algorithm that computes the longest substring palindromes (LSPals) of a given string in O(n) time, where n is the length of the string. In this paper, we consider the problem of finding the LSPal after the string is edited. We present an algorithm that uses O(n) time and space for preprocessing, and answers the length of the LSPals in O(l + log log n) time, after a substring in T is replaced by a string of arbitrary length l. This outperforms the query algorithm proposed in our previous work [CPM 2018] that uses O(l + log n) time for each query.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial algorithms
Keywords
  • palindromes
  • string algorithm
  • periodicity

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References

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