Parameterized Complexity of (d,r)-Domination via Modular Decomposition

TL;DR

This paper investigates the parameterized complexity of the extsc{$(d,r)$-Domination} problem, a generalization of domination in graphs, providing fixed-parameter algorithms and kernelizations for certain variants.

Contribution

It introduces the extsc{$(d,r)$-Domination} problem and analyzes its complexity, offering new algorithms and kernelization results for various parameter settings.

Findings

Fixed-parameter algorithms developed for some variants.

Polynomial kernelizations achieved for certain parameters.

Complexity results inform strategies for misinformation containment.

Abstract

With the rise of social media, misinformation has significant negative effects on the decision-making of individuals, organizations and communities within society. Identifying and mitigating the spread of fake information is a challenging issue. We consider a generalization of the Domination problem that can be used to detect a set of individuals who, through an awareness process, can prevent the spreading of fake narratives. The considered problem, named \textsc{$(d,r)$-Domination} generalizes both distance and multiple domination. We study the parameterized complexity of the problem according to standard and structural parameters. We give fixed-parameter algorithms as well as polynomial compressions/kernelizations for some variants of the problem and parameter combinations.