Learning and Maximizing Influence in Social Networks Under Capacity Constraints

Influence maximization (IM) refers to the problem of finding a subset of nodes in a network through which we could maximize our reach to other nodes in the network. This set is often called the "seed set", and its constituent nodes maximize the social diffusion process. IM has previously been studied in various settings, including under a time deadline, subject to constraints such as that of budget or coverage, and even subject to measures other than the centrality of nodes. The solution approach has generally been to prove that the objective function is submodular, or has a submodular proxy, and thus has a close greedy approximation. In this paper, we explore a variant of the IM problem where we wish to reach out to and maximize the probability of infection of a small subset of bounded capacity K. We show that this problem does not exhibit the same submodular guarantees as the original IM problem, for which we resort to the theory of gamma-weakly submodular functions. Subsequently, we develop a greedy algorithm that maximizes our objective despite the lack of submodularity. We also develop a suitable learning model that out-competes baselines on the task of predicting the top-K infected nodes, given a seed set as input.