Computing Palindromic Factorizations and Palindromic Covers On-line

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A palindromic factorization of a string w is a factorization of w consisting only of palindromic substrings of w. In this paper, we present an on-line O(n logn)-time O(n)-space algorithm to compute smallest palindromic factorizations of all prefixes of w, where n is the length of a given string w. We then show how to extend this algorithm to compute smallest maximal palindromic factorizations of all prefixes of w, consisting only of maximal palindromes (non-extensible palindromic substring) of each prefix, in O(n logn) time and O(n) space, in an on-line manner. We also present an on-line O(n)-time O(n)-space algorithm to compute a smallest palindromic cover of w.