A subquadratic algorithm for minimum palindromic factorization

We give an O(nlog⁡n)O(nlog⁡n)-time, O(n)O(n)-space algorithm for factoring a string into the minimum number of palindromic substrings. That is, given a string S[1..n]S[1..n], in O(nlog⁡n)O(nlog⁡n) time our algorithm returns the minimum number of palindromes S1,…,SℓS1,…,Sℓ such that S=S1⋯SℓS=S1⋯Sℓ. We also show that the time complexity is O(n)O(n) on average and Ω(nlog⁡n)Ω(nlog⁡n) in the worst case. The last result is based on a characterization of the palindromic structure of Zimin words.