Counting and Verifying Maximal Palindromes

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.

• Type: Journal
• Year: 2010
• Where: SPIRE
• Authors: Tomohiro I, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
• Keywords: Information Technology, Maximal Palindromes, Palindromes, SPIRE 2010, String