Seed Activation Scheduling for Influence Maximization in Social Networks

Abstract

This paper addresses the challenge of strategically maximizing the influence spread in a social network, by exploiting cascade propagators termed “seeds”. It introduces the Seed Activation Scheduling Problem (SASP) that chooses the timing of seed activation under a given budget, over a given time horizon, in the presence/absence of competition. The SASP is framed as a blogger-centric marketing problem on a two-level network, where the decisions are made to buy sponsored posts from prominent bloggers at calculated points in time. A Bayesian evidence diffusion model – the Partial Parallel Cascade (PPC) model – allows the network nodes to be partially activated, proportional to their accumulated evidence levels. The SASP under the PPC model is proven NP-hard. A mixed-integer program is presented for the SASP, along with an efficient column generation heuristic. The paper sets up its problem instances in real-world settings, taking web-based marketing as an application example. Favorable optimality gaps are achieved for SASP solutions on networks based on observed user interactions in pro-health discussion forums. The presented analyses highlight a trade-off between early and late seed activation in igniting and maintaining influence cascades over time. The results reveal the importance of early seeds for campaigns that favor longevity, e.g., in service industry, and the importance of late seeds for campaigns with deadline(s), e.g., in political competitions.