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We consider ad hoc wireless networks that are configured as Mobile Backbone Networks. A hierarchical network architecture is synthesized, consisting of Access Nets (ANets) and Backbone Nets (BNets). Each ANet is managed by a (dynamically elected) Backbone Node (BN) that is equipped with higher capability (transmission and processing) modules. The BNs are chosen from currently active mobile backbone-capable nodes or are represented by (ground and/or airborne) unmanned vehicles (UVs) that are guided into selected positions. We develop and investigate a new joint power controlled medium access control (MAC) algorithm for wireless access nets (ANets). Under our new protocol, the net backbone node instructs the ANet nodes to make power control adjustments while simultaneously allocating to them slots for the requested transmissions of their packets. This algorithm, in contrast to other employed conventional graph-based scheduling algorithms, satisfies the requirement that a minimum signal-to-interference and noise ratio (SINR) is met at all intended receivers. We show our algorithm to lead to a significant increase in the net throughput level by attaining high spatial reuse.