Distance Vector Domination

TL;DR

Distance Vector Domination is a generalized graph problem aimed at identifying key individuals to immunize in social networks to prevent fake information spread, with complexity results and algorithms provided.

Contribution

It introduces the Distance Vector Domination problem, extending distance and multiple domination, and analyzes its parameterized complexity with new algorithms and hardness results.

Findings

W[1]-hardness with respect to neighborhood diversity

Fixed-parameter algorithms for certain variants

Complexity analysis of the generalized domination problem

Abstract

Identifying and mitigating the spread of fake information is a challenging issue that has become dominant with the rise of social media. We consider a generalization of the Domination problem that can be used to detect a set of individuals who, once immunized, can prevent the spreading of fake narratives. The considered problem, named {\em Distance Vector Domination} generalizes both distance and multiple domination, at individual (i.e., vertex) level. We study the parameterized complexity of the problem according to several standard and structural parameters. We prove the W[1]-hardness of the problem with respect to neighborhood diversity, even when all the distances are $1$. We also give fixed-parameter algorithms for some variants of the problem and parameter combinations.