Palindromic Length in Linear Time

Palindromic k-Factorization in Pure Linear Time

“…. , w k are palindromes, is a palindromic (k-)factorization of s. Efficient algorithms for palindromic factorization [3,4,9,11,13] used the following (or very similar) combinatorial properties. Lemma 3 ([11,Lemma 7]).…”

“…Due to symmetry, we always write pl j assuming j ∈ {0, 1}. The algorithm, which is a straightforward adaptation of the algorithm of [3] for palindromic length, serves as a base for the linear-time solution, so we provide necessary details. We rewrite rule (1) as…”

“…Proof. The lemma appeared in [3] without a proof, so we provide it here. If p = 1, 3) trivially holds, so let p > 1.…”

“….n] = aabaaba and left [3] = n − 7. If we extend s by b, this will break period 3 and make left [3] undefined.…”

“…On algorithmic side, the palindromic length of a string of length n was shown to be computable in O(n log n) time [4,9,13]. In [3], the optimal O(n) bound was reached, using bit compression and range operations.…”