Characterize approximate monotonicity and submodularity regimes in the PT model

Characterize structural or parameter-dependent regimes in which the Pressure Threshold (PT) influence function exhibits approximate monotonicity or submodularity, thereby enabling stronger guarantees for greedy influence maximization and potentially recovering classical (1-1/e)-type approximation guarantees.

Background

The paper introduces the Pressure Threshold (PT) diffusion model, in which a node's outgoing influence is amplified according to the cumulative social pressure that caused its activation. This reinforcement mechanism makes the influence-maximization objective generally non-monotone and non-submodular when the amplification parameter is positive, so classical greedy approximation guarantees do not directly apply.

The authors develop a sandwich approximation framework using monotone submodular lower- and upper-bounding models, but leave unresolved the broader characterization of conditions under which the PT objective itself retains approximate monotonicity or submodularity. Establishing such structural or parameter-dependent conditions would clarify when reinforcement remains compatible with efficient optimization and when classical approximation guarantees can be recovered.

References

On the theoretical side, an important question is to characterize regimes in which the PT influence function exhibits approximate monotonicity or submodularity, enabling stronger guarantees for greedy optimization. Identifying structural or parameter-dependent conditions under which classical %$(1 - 1/e)$-type approximation guarantees can be recovered remains an open challenge.

— How Social Reinforcement Shapes Word-of-Mouth: A Conviction-Based Model for Marketing Diffusion and Network Targeting  (2610.13890 - Umrawal et al., 9 Oct 2026) in Section "Future Research" (Conclusion)