Parameterized Tractability of the Maximum-Duo Preservation String Mapping Problem

TL;DR

This paper explores the fixed-parameter tractability of the Maximum-Duo Preservation String Mapping Problem, providing a color-coding based algorithm and a polynomial kernel of size O(k^6).

Contribution

It introduces the first fixed-parameter algorithm and kernelization results for the problem, advancing understanding of its computational complexity.

Findings

The problem is fixed-parameter tractable when parameterized by k.

A color-coding based algorithm is developed for the problem.

A polynomial kernel of size O(k^6) is constructed.

Abstract

In this paper we investigate the parameterized complexity of the Maximum-Duo Preservation String Mapping Problem, the complementary of the Minimum Common String Partition Problem. We show that this problem is fixed-parameter tractable when parameterized by the number k of conserved duos, by first giving a parameterized algorithm based on the color-coding technique and then presenting a reduction to a kernel of size O(k^6 ).