Efficient computation of longest single-arm-gapped palindromes in a string

Shintaro Narisada, Diptarama Hendrian, Kazuyuki Narisawa, Shunsuke Inenaga, Ayumi Shinohara

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


In this paper, we introduce new types of approximate palindromes called single-arm-gapped palindromes (shortly SAGPs). A SAGP contains a gap in either its left or right arm, which is in the form of either wgucuRwR or wucuRgwR, where w and u are non-empty strings, wR and uR are respectively the reversed strings of w and u, g is a string called a gap, and c is either a single character or the empty string. Here we call wu and uRwR the arm of the SAGP, and |uv| the length of the arm. We classify SAGPs into two groups: those which have ucuR as a maximal palindrome (type-1), and the others (type-2). We propose several algorithms to compute type-1 SAGPs with longest arms occurring in a given string, based on suffix arrays. Then, we propose a linear-time algorithm to compute all type-1 SAGPs with longest arms, based on suffix trees. Also, we show how to compute type-2 SAGPs with longest arms in linear time. We also perform some preliminary experiments to show practical performances of the proposed methods.

Original languageEnglish
Pages (from-to)160-173
Number of pages14
JournalTheoretical Computer Science
Publication statusPublished - 2020 Apr 6


  • Palindromes
  • String algorithms
  • Suffix arrays
  • Suffix trees


Dive into the research topics of 'Efficient computation of longest single-arm-gapped palindromes in a string'. Together they form a unique fingerprint.

Cite this