TY - JOUR

T1 - Revisiting the parameterized complexity of Maximum-Duo Preservation String Mapping

AU - Komusiewicz, Christian

AU - de Oliveira Oliveira, Mateus

AU - Zehavi, Meirav

N1 - Publisher Copyright:
© 2020 Elsevier B.V.

PY - 2020/12/22

Y1 - 2020/12/22

N2 - 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 4k⋅nO(1) time, and a deterministic algorithm that solves this problem in 6.855k⋅nO(1) time. The previous best known (deterministic) algorithm for this problem has (8e)2k+o(k)⋅nO(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).

AB - 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 4k⋅nO(1) time, and a deterministic algorithm that solves this problem in 6.855k⋅nO(1) time. The previous best known (deterministic) algorithm for this problem has (8e)2k+o(k)⋅nO(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).

KW - Kernelization

KW - Maximum-Duo Preservation String Mapping

KW - Parameterized algorithms

UR - http://www.scopus.com/inward/record.url?scp=85091514099&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2020.09.034

DO - 10.1016/j.tcs.2020.09.034

M3 - Article

AN - SCOPUS:85091514099

VL - 847

SP - 27

EP - 38

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -