Targeting influence in a harmonic opinion model

Fuente: arXiv
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Main Authors: Boyd, Zachary M., Fraiman, Nicolas, Marzuola, Jeremy L., Mucha, Peter J., Osting, Braxton
Format: Preprint
Published: 2024
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_version_ 1866909234389581824
author Boyd, Zachary M.
Fraiman, Nicolas
Marzuola, Jeremy L.
Mucha, Peter J.
Osting, Braxton
author_facet Boyd, Zachary M.
Fraiman, Nicolas
Marzuola, Jeremy L.
Mucha, Peter J.
Osting, Braxton
contents Influence propagation in social networks is a central problem in modern social network analysis, with important societal applications in politics and advertising. A large body of work has focused on cascading models, viral marketing, and finite-horizon diffusion. There is, however, a need for more developed, mathematically principled \emph{adversarial models}, in which multiple, opposed actors strategically select nodes whose influence will maximally sway the crowd to their point of view. In the present work, we develop and analyze such a model based on harmonic functions and linear diffusion. We prove that our general problem is NP-hard and that the objective function is monotone and submodular; consequently, we can greedily approximate the solution within a constant factor. Introducing and analyzing a convex relaxation, we show that the problem can be approximately solved using smooth optimization methods. We illustrate the effectiveness of our approach on a variety of example networks.
format Preprint
id arxiv_https___arxiv_org_abs_2407_00213
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Targeting influence in a harmonic opinion model
Boyd, Zachary M.
Fraiman, Nicolas
Marzuola, Jeremy L.
Mucha, Peter J.
Osting, Braxton
Social and Information Networks
Numerical Analysis
Probability
35J05, 05C50, 49M41, 65K10
Influence propagation in social networks is a central problem in modern social network analysis, with important societal applications in politics and advertising. A large body of work has focused on cascading models, viral marketing, and finite-horizon diffusion. There is, however, a need for more developed, mathematically principled \emph{adversarial models}, in which multiple, opposed actors strategically select nodes whose influence will maximally sway the crowd to their point of view. In the present work, we develop and analyze such a model based on harmonic functions and linear diffusion. We prove that our general problem is NP-hard and that the objective function is monotone and submodular; consequently, we can greedily approximate the solution within a constant factor. Introducing and analyzing a convex relaxation, we show that the problem can be approximately solved using smooth optimization methods. We illustrate the effectiveness of our approach on a variety of example networks.
title Targeting influence in a harmonic opinion model
topic Social and Information Networks
Numerical Analysis
Probability
35J05, 05C50, 49M41, 65K10
url https://arxiv.org/abs/2407.00213