This paper investigates quality of service (QoS)-aware relay selection and subcarrier assignment in multiuser OFDMA relay networks. In contrast to some existing works, which solve the sum-rate maximization problem directly, we first simplify it by exploiting the structure of the optimal solution and then consider the simplified problem from the perspectives of both primal and dual optimality. To characterize the optimal sum-rate performance, we solve the simplified problem optimally by the branch-and-cut method. In addition to the sum-rate maximization problem, we demonstrate that its two variants, namely, the worst-user rate maximization problem and the mixed rate maximization problem, can be also similarly simplified and then solved optimally by the branch-and-cut method. The optimal method serving as the benchmark is particularly suitable for problems of moderate scale. Furthermore, we study the simplified sum-rate maximization problem comprehensively from a dual perspective and propose three types of subgradient methods for the dual problem. The dual subgradient methods obtaining near-optimal solutions can be implemented in a distributed manner and thus are quite suitable for high-dimensional problems. To provide more in-depth analysis, we further consider the scenario in which subcarrier pairing is incorporated and suggest the natural generalization from the one-source-node case to the multiple-source-node case. Finally, two groups of simulations are conducted to validate the optimality of the branch-and-cut method and the effectiveness of the dual subgradient methods.
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