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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Bibliographic Details
Published in:	Discrete mathematics and theoretical computer science Vol. 26:2; no. Discrete Algorithms
Main Authors:	Dvořák, Michal, Knop, Dušan, Schierreich, Šimon
Format:	Journal Article
Language:	English
Published:	Discrete Mathematics & Theoretical Computer Science 21.08.2024
Subjects:	computer science - computational complexity
ISSN:	1365-8050, 1365-8050
Online Access:	Get full text
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Summary:	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.
ISSN:	1365-8050 1365-8050
DOI:	10.46298/dmtcs.11591