Computing longest palindromic substring after single-character or block-wise edits

Palindromes are important objects in strings which have been extensively studied from combinatorial, algorithmic, and bioinformatics points of views. It is known that the length longest palindromic substrings (LPSs) a given string T n can be computed O(n) time by Manacher's algorithm [12]. In this paper, we consider problem finding LPS after edited. We present an uses space for preprocessing, answers LPSs O(log⁡(min⁡{σ,log⁡n})) single character substitution, insertion, or deletion, where σ denotes number distinct characters appearing T. also propose O(ℓ+log⁡log⁡n) time, existing substring replaced arbitrary ℓ.