Intervention problems in the Linear Threshold Model: A general formulation and new results

2026-09-15

AI Summary

研究线性阈值模型中的最优干预问题，通过引入有向路径数概念来最小化确保全局收敛到全1配置的干预成本。

Abstract

We study an optimal intervention problem for linear threshold models. This is a popular class of dynamical network systems whereby a number of agents, identified with the nodes of a graph, strategically change their binary action (0 or 1) according to a threshold rule. Specifically, an agent adopts action 1 if and only if the fraction of its neighbors in the interaction graph that do so is greater than or equal to a prescribed threshold. Assuming that a planner can modify the agents' thresholds at a cost equal to the aggregate threshold increase, we study the minimum intervention cost needed to ensure global convergence to the all-1 configuration. Our main contribution is the introduction of a new graph-theoretic quantity, called oriented path number, that is the minimum number of disjoint paths needed to cover the graph that can be oriented to form a directed acyclic graph. When thresholds are all equal to 1/2, the optimal cost is shown to coincide with the oriented path number, whereas, in the general case, it turns out to be the main ingredient of a bound on the optimal intervention cost.

Problem

• Linear Threshold Model
• Optimal Intervention
• Threshold Modification
• Global Convergence

Innovation

• oriented path number
• linear threshold model
• optimal intervention cost