On the Complexity of Target Set Selection in Simple Geometric Networks

We study the following model of disease spread in a social network. At first, all individuals are either infected or healthy. Next, in discrete rounds, the disease spreads in the network from infected to healthy individuals such that a healthy individual gets infected if and only if a sufficient num...

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Veröffentlicht in:arXiv.org
Hauptverfasser: Dvořák, Michal, Knop, Dušan, Šimon Schierreich
Format: Paper
Sprache:Englisch
Veröffentlicht: Ithaca Cornell University Library, arXiv.org 04.07.2024
Schlagworte:
Graphical representations
Graphs
Social networks
Vertex sets
ISSN:2331-8422
Online-Zugang:Volltext
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Zusammenfassung:We study the following model of disease spread in a social network. At first, all individuals are either infected or healthy. Next, in discrete rounds, the disease spreads in the network from infected to healthy individuals such that a healthy individual gets infected if and only if a sufficient number of its direct neighbors are already infected. We represent the social network as a graph. Inspired by the real-world restrictions in the current epidemic, especially by social and physical distancing requirements, we restrict ourselves to networks that can be represented as geometric intersection graphs. We show that finding a minimal vertex set of initially infected individuals to spread the disease in the whole network is computationally hard, already on unit disk graphs. Hence, to provide some algorithmic results, we focus ourselves on simpler geometric graph classes, such as interval graphs and grid graphs.
Bibliographie:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.2307.06976