Targeting influence in a harmonic opinion model
<|reference_start|>Targeting influence in a harmonic opinion model: 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.<|reference_end|>
@article{boyd2024targeting,
    title={Targeting influence in a harmonic opinion model},
    author={Zachary M. Boyd and Nicolas Fraiman and Jeremy L. Marzuola and Peter
  J. Mucha and Braxton Osting},
    journal={arXiv preprint arXiv:2407.00213},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.00213},
    primaryClass={cs.SI cs.NA math.NA math.PR}
}