Revisiting the parameterized complexity of Maximum-Duo Preservation String Mapping

Abstract

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 time 4 k • n O(1) , and a deterministic algorithm that solves this problem in time 6.855 k • n O(1) . The previous best known (deterministic) algorithm for this problem has running time (8e) 2k+o(k) • n O(1) [Beretta et al., Theor. Comput. Sci. 2016]. We also show that Max-Duo PSM admits a problem kernel of size O(k 3 ), improving upon the previous best known problem kernel of size O(k 6 ).