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This paper describes new algorithms for throughput optimization in a mobile backbone network. This hierarchical communication framework combines mobile backbone nodes, which have superior mobility and communication capability, with regular nodes, which are constrained in mobility and communication capability. An important quantity of interest in mobile backbone networks is the number of regular nodes that can be successfully assigned to mobile backbone nodes at a given throughput level. This paper develops a novel technique for maximizing this quantity in networks of fixed regular nodes using mixed-integer linear programming (MILP). The MILP-based algorithm provides a significant reduction in computation time compared to existing methods and is computationally tractable for problems of moderate size. An approximation algorithm is also developed that is appropriate for large-scale problems. This paper presents a theoretical performance guarantee for the approximation algorithm and also demonstrates its empirical performance. Finally, the mobile backbone network problem is extended to include mobile regular nodes, and exact and approximate solution algorithms are presented for this extension.