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Mobile Backbone Networks are heterogeneous wireless networks in which a subset of the nodes are more capable than others. The more capable nodes are referred to as Mobile Backbone Nodes (MBNs), whose primary role is to provide a mobile infrastructure in order to facilitate reliable end-to-end communication between nodes in the Network. In this paper, we consider the problem of optimally placing the MBNs over a finite time horizon. Specifically, we consider the path planning of a single MBN and aim to maximize the time-average system throughput. We present a discrete problem formulation, and develop an optimal solution for the single step velocity-constrained MBN placement problem. Using this as a sub-routine, we provide a greedy heuristic algorithm for the overall path planning problem. Next, we develop a dynamic programming based approximation algorithm for the problem. Finally, we compare the developed approaches via simulation.