## 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 (8e)^{2k+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}).

Original language | English |
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Pages (from-to) | 27-38 |

Number of pages | 12 |

Journal | Theoretical Computer Science |

Volume | 847 |

DOIs | |

State | Published - 22 Dec 2020 |

## Keywords

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

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science