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In recent years, we have seen a surge of interest in enabling communications over meshed wireless networks. Particularly, supporting peer-to-peer communications over a multi-hop wireless network has a big potential in enabling ubiquitous computing. However, many wireless nodes have limited capabilities, for example, sensor nodes or small handheld devices. Also, the end-to-end capacity and delay degrade significantly as the path length increases with the number of network nodes. In these scenarios, the deployment of a backbone network could potentially facilitate higher performance network communications. In this paper, we study the novel Reinforcement Back-bone Network (RBN) deployment problem considering the practical limitation in the number of available backbone nodes and enforcing backbone network connectivity. We propose an iterative and adaptive (ITA) algorithm for efficient backbone network deployment. In addition, in order to provide the performance bound, we redefine and solve the problem by implementing the Generic Algorithm. Finally, we present our simulation results under various settings and compare the performance of the proposed ITA algorithm and the generic algorithm. Our study indicates that the proposed ITA algorithm is promising for deploying a connected RBN with a limited number of available backbone nodes.