Optimal Interventions on the Linear Threshold Model in Large-Scale Networks

2026-05-11

AI Summary

This work addresses the minimum-cost intervention problem under the linear threshold model in large-scale networks—specifically, achieving a target state in at least a prescribed fraction of nodes within a finite number of steps at minimal cost. For the first time, it proposes a scalable approximation method that operates solely with network statistical information, without requiring full topological knowledge. The approach leverages local mean-field approximation to reformulate the original problem as a linear program with infinitely many constraints, which is then efficiently solved via a finite-dimensional linear programming relaxation. Experimental evaluations on real-world networks demonstrate that the proposed method significantly outperforms existing state-of-the-art algorithms for both optimal seed selection and minimum-cost influence maximization.

Abstract

We study an optimal intervention problem on the linear threshold model (LTM) in which a social planner aims to design minimal-cost interventions that modify the agents' thresholds, under the constraint that at least a predefined fraction of agents reaches a given state after a finite number of iterations. While this problem is known to be NP-hard and its exact solution requires full knowledge of the network structure, we focus on approximate solutions for large-scale networks and assume that the planner has only statistical knowledge of the network. In particular, we build on a local mean-field approximation of the LTM that is known to hold true on large-scale random networks, and reformulate the optimal intervention problem as a linear program with an infinite set of constraints. We then show how to approximate the solutions of the latter problem by standard linear programs with finitely many constraints. Finally, our approach is validated through numerical experiments on real-world networks and compared both with optimal seeding and state-of-the-art algorithms for the least-cost influence.

Problem

• linear threshold model
• optimal intervention
• large-scale networks
• threshold modification
• influence propagation

Innovation

• linear threshold model
• optimal intervention
• mean-field approximation
• large-scale networks
• linear programming