Counting and Verifying Maximal Palindromes

  • Tomohiro I
  • Shunsuke Inenaga
  • Hideo Bannai
  • Masayuki Takeda
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6393)

Abstract

A palindrome is a symmetric string that reads the same forward and backward. Let pals(w) denote the set of maximal palindromes of a string w in which each palindrome is represented by a pair (c, r), where c is the center and r is the radius of the palindrome. We say that two strings w and z are pal-distinct if pals(w) ≠ pals(z). Firstly, we describe the number of pal-distinct strings, and show that we can enumerate all pal-distinct strings in time linear in the output size, for alphabets of size at most 3. These results follow from a close relationship between maximal palindromes and parameterized matching. Secondly, we present a linear time algorithm which finds a string w such that pals(w) is identical to a given set of maximal palindromes.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Tomohiro I
    • 1
  • Shunsuke Inenaga
    • 2
  • Hideo Bannai
    • 1
  • Masayuki Takeda
    • 1
  1. 1.Department of InformaticsKyushu UniversityJapan
  2. 2.Graduate School of Information Science and Electrical EngineeringKyushu UniversityFukuokaJapan

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