We study a novel hierarchical wireless networking approach in which some of the nodes are more capable than others. In such networks, the more capable nodes can serve as Mobile Backbone Nodes and provide a backbone over which end-toend communication can take place. Our approach consists of controlling the mobility of the Backbone Nodes in order to maintain connectivity. We formulate the problem of minimizing the number of backbone nodes and refer to it as the Connected Disk Cover problem. We show that it can be decomposed into the Geometric Disk Cover (GDC) problem and the Steiner Tree Problem with Minimum Number of Steiner Points (STP-MSP). We prove that if these subproblems are solved separately by - and -approximation algorithms, the approximation ratio of the joint solution is +. Then, we focus on the two subproblems and present a number of distributed approximation algorithms that maintain a solution to the GDC problem under mobility. A new approach to the solution of the STP-MSP...