Efficient Algorithms for Influence Maximization in General Models and Observed Cascades

2026-06-20

AI Summary

This work addresses the influence maximization problem under general stochastic diffusion models—specifically the Observation Cascade Model (OCM) and the Independent Cascade Model (ICM)—where only black-box sampling access to the propagation process is available, leading to significant computational bottlenecks. To overcome this challenge, the authors propose a low-adaptivity optimization framework that integrates an empirical variance-guided adaptive sampling strategy with sketching techniques. Their approach yields the first near-linear-time algorithm for OCM with provable theoretical guarantees. For ICM, it substantially reduces sample complexity by replacing the dependence on the number of nodes \(n\) with the diffusion depth \(\tau\). Theoretical analysis demonstrates that the algorithm achieves near-optimal approximation quality while operating within a logarithmic factor of the best possible runtime efficiency.

Abstract

We study influence maximization in general stochastic models, the observed cascades model, and the independent cascade (IC) model. For general stochastic models with only black-box sample access, we introduce a low-adaptivity optimization framework that improves sample complexity and running time over Sadeh et al. (2020) and is instrumental to all our results. We further introduce an adaptive algorithm guided by empirical variance, avoiding pessimistic worst-case bounds. Combining our optimization framework with sketching, we obtain the first algorithm with provable guarantees and nearly-linear running time for influence maximization on observed cascades, optimal up to logarithmic factors. For IC, we prove a novel tail bound replacing a factor $n$ with $τ$ (the number of diffusion steps) in sample complexity, improving over prior work when $τ$ is small, as is common due to small-world phenomena. Experiments confirm substantial speedups while maintaining solution quality.

Problem

• influence maximization
• stochastic models
• observed cascades
• independent cascade model
• sample complexity

Innovation

• low-adaptivity optimization
• observed cascades
• influence maximization
• sample complexity
• empirical variance