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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Published in:arXiv.org
Main Authors: Dvořák, Michal, Knop, Dušan, Šimon Schierreich
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 04.07.2024
Subjects:
Graphical representations
Graphs
Social networks
Vertex sets
ISSN:2331-8422
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Abstract 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.
AbstractList 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.
Author Dvořák, Michal
Knop, Dušan
Šimon Schierreich
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  fullname: Šimon Schierreich
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Graphs
Social networks
Vertex sets
Title On the Complexity of Target Set Selection in Simple Geometric Networks
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