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We propose and analyze a new class of controlled multi-type branchingprocesses with a per-step linear resource constraint, motivated by potentialapplications in viral marketing and cancer treatment. We show that the optimalexponential growth rate of the population can be achieved by maintaining afixed proportion among the species, for both deterministic and stochasticbranching processes. In the special case of a two-type population and with asymmetric reward structure, the optimal proportion is obtained in closed-form.  In addition to revealing structural properties of controlled branchingprocesses, our results are intended to provide the practitioners with aneasy-to-interpret benchmark for best practices, if not exact policies. As aproof of concept, the methodology is applied to the linkage structure of the2004 US Presidential Election blogosphere, where the optimal growth ratedemonstrates sizable gains over a uniform selection strategy, and to atwo-compartment cell-cycle kinetics model for cancer growth, with realisticparameters, where the robust estimate for minimal treatment intensity under aworst-case growth rate is noticeably more conservative compared to thatobtained using more optimistic assumptions.

Go Viral, or Not: Rate-Optimal Control for Resource-Constrained Branching Processes