Fractional Budget Allocation for Influence Maximization

We consider a generalization of the widely studied discrete influence maximization problem. We consider that instead of marketers using a budget to send free products to a few influencers, they can provide discounts to partly incentivize a larger set of influencers with the same budget. We show that this problem is an instance of maximizing the multilinear extension of a monotone submodular set function subject to an L-1 constraint. We propose and analyze an efficient (1 - 1/e)-approximation algorithm. We run experiments on a real-world social network to show the performance of our method in contrast to methods proposed for other generalizations of influence maximization.