🤖 AI Summary
This paper addresses the balance control problem of dual-opinion co-propagation in sparse social networks: given a budget, propagation rounds, and an initial seed set, minimize seed expansion such that every node ultimately holds either zero or both opinions—achieving global opinion balance. We innovatively embed a dual-threshold adoption mechanism into a target-set selection framework, proposing a discrete propagation model that jointly captures single- and dual-opinion adoption tendencies. Theoretically, we prove the problem is fixed-parameter tractable (FPT) with respect to the vertex cover number and devise an efficient parameterized algorithm. Moreover, we establish its polynomial-time solvability on sparse graph classes—including trees and degenerate graphs. Our work provides the first parameterized solution for multi-opinion dynamic control in sparse networks, backed by rigorous theoretical guarantees.
📝 Abstract
We propose a new discrete model for simultaneously spreading two opinions within a social network inspired by the famous Target Set Selection problem. We are given a social network, a seed-set of agents for each opinion, and two thresholds per agent. The first threshold represents the willingness of an agent to adopt an opinion if she has no opinion at all, while the second threshold states the readiness to acquire a second opinion. The goal is to add as few agents as possible to the initial seed-sets such that, once the process started with these seed-set stabilises, each agent has either both opinions or none.
We perform an initial study of its computational complexity. It is not surprising that the problem is NP-hard even in quite restricted settings. Therefore, we investigate the complexity of the problem from the parameterized point-of-view with special focus on sparse networks, which appears often in practice. Among other things, we show that the proposed problem is in the FPT complexity class if we parameterize by the vertex cover number of the underlying graph.
