Revisiting the parameterized complexity of Maximum-Duo Preservation String Mapping

In the MAXIMUM-DUO PRESERVATION STRING MAPPING (MAX-DUO PSM) problem, the input consists of two related strings A and B of length n and a nonnegative integer k. The objective is to determine whether there exists a mapping m from the set of positions of A to the set of positions of B that maps only to positions with the same character and preserves at least k duos, which are pairs of adjacent positions. We develop a randomized algorithm that solves MAX-DUO PSM in 4^k⋅n^O(1) time, and a deterministic algorithm that solves this problem in 6.855^k⋅n^O(1) time. The previous best known (deterministic) algorithm for this problem has (8e)^2k+o(k)⋅n^O(1) running time [Beretta et al. (2016) [1,2]]. We also show that MAX-DUO PSM admits a problem kernel of size O(k³), improving upon the previous best known problem kernel of size O(k⁶).