Parameterized Complexity of (d,r)-Domination via Modular Decomposition
Gennaro Cordasco, Luisa Gargano, Adele A. Rescigno
TL;DR
This work studies the parameterized complexity of $(d,r)$-Domination, a generalization of domination that combines distance and multiplicity, with motivation from mitigating misinformation spread. It leverages modular decomposition and power-graph techniques to derive FPT results and kernelizations for several structural parameters, including ${mw}$, ${itp}$, and ${nd}$. The authors provide a DP/ILP-based fixed-parameter algorithm for ${mw}+d$, a polynomial compression for $(1,r)$-Domination under connectedness, a PC for $(d,r)$-Domination parameterized by ${itp}+d$, and a polynomial kernel for ${nd}+d$ by modular pruning. Collectively, these results advance tractability for $(d,r)$-Domination under structural graph parameters and offer practical preprocessing and decomposition strategies for related network problems.
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.