  Connectivity - or the lack thereof - is crucial for the function of many
man-made systems, from financial and economic networks over epidemic spreading
in social networks to technical infrastructure. Often, connections are
deliberately established or removed to induce, maintain, or destroy global
connectivity. Thus, there has been a great interest in understanding how to
control percolation, the transition to large-scale connectivity. Previous work,
however, studied control strategies assuming unlimited resources. Here, we
depart from this unrealistic assumption and consider the effect of limited
resources on the effectiveness of control. We show that, even for scarce
resources, percolation can be controlled with an efficient intervention
strategy. We derive this strategy and study its implications, revealing a
discontinuous transition as an unintended side-effect of optimal control.
