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 MaxDuo PSM in time 4 · nO(1), and a deterministic algorithm that solves this problem in time 6.855 · nO(1). The previous best known (deterministic) algorithm for this problem has running time (8e)2k+o(k) ·nO(1) [Beretta et al., Theor. Comput. Sci. 2016]. 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). 1998 ACM Subject Classification G.2.1 Combinatorics, F.2 Analysis of Algorithms and Problem Complexity