Longest Palindromic Substring in Sublinear Time

We revisit the classic algorithmic problem of computing a longest palidromic substring. This problem is solvable by a celebrated ?(n)-time algorithm [Manacher, J. ACM 1975], where n is the length of the input string. For small alphabets, ?(n) is not necessarily optimal in the word RAM model of computation: a string of length n over alphabet [0,?) can be stored in ?(n log ?/log n) space and read in ?(n log ?/log n) time. We devise a simple ?(n log ?/log n)-time algorithm for computing a longest palindromic substring. In particular, our algorithm works in sublinear time if ? = 2^{o(log n)}. Our technique relies on periodicity and on the ?(n log ?/log n)-time constructible data structure of Kempa and Kociumaka [STOC 2019] that answers longest common extension queries in ?(1) time