Revisiting the parameterized complexity of Maximum-Duo Preservation String Mapping

Christian Komusiewicz, Mateus de Oliveira Oliveira, Meirav Zehavi

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 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).

Original languageEnglish
Pages (from-to)27-38
Number of pages12
JournalTheoretical Computer Science
Volume847
DOIs
StatePublished - 22 Dec 2020

Keywords

  • Kernelization
  • Maximum-Duo Preservation String Mapping
  • Parameterized algorithms

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