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Stochastically assembled nanoscale architectures have the potential to achieve device densities 100 times greater than today's CMOS. A key challenge facing nanotechnologies is controlling parallel sets of nanowires (NWs), such as those in crossbars, using a moderate number of mesoscale wires. Three similar methods have been proposed to control NWs using a set of perpendicular mesoscale wires. The first is based on NW differentiation during manufacture, the second makes random connections between NWs and mesoscale wires, and the third, a mask-based approach, interposes high-K dielectric regions between NWs and mesoscale wires. Each of these addressing schemes involves a stochastic step in their implementation. In this paper, we analyze the mask-based approach and show that, when compared to the other two schemes, a large number of mesoscale control wires are necessary for its realization.