Revisiting the Parameterized Complexity of Maximum-Duo Preservation String Mapping

Abstract

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 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 ( 8 e ) 2 k + 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 ( k 3 ) , improving upon the previous best known problem kernel of size O ( k 6 ) .