  In this paper, we study influence maximization in the voter model in the
presence of biased voters (or zealots) on complex networks. Under what
conditions should an external controller with finite budget who aims at
maximizing its influence over the system target zealots? Our analysis, based on
both analytical and numerical results, shows a rich diagram of preferences and
degree-dependencies of allocations to zealots and normal agents varying with
the budget. We find that when we have a large budget or for low levels of
zealotry, optimal strategies should give larger allocations to zealots and
allocations are positively correlated with node degree. In contrast, for low
budgets or highly-biased zealots, optimal strategies give higher allocations to
normal agents, with some residual allocations to zealots, and allocations to
both types of agents decrease with node degree. Our results emphasize that
heterogeneity in agent properties strongly affects strategies for influence
maximization on heterogeneous networks.
