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In this paper, we study resource scheduling in a relay-assisted cognitive radio network with the orthogonal frequency division multiple access (OFDMA) scheme adopted to cope with the multi-user configuration. We discuss the optimization over the relay assignment, subcarrier allocation, per-node power control, and heterogenous quality-of-service (QoS) provisioning. The discrete characters of relay assignment and subcarrier allocation lead to a mixed integer nonlinear program (MINLP) whose computational complexity grows exponentially with the number of subcarriers. In an attempt to treat this complication, an asymptotically optimal solution based on the dual-analysis framework is proposed, for which we investigate the optimality of the dual method in the two scenarios: with and without subcarrier pairing. For both cases, it is shown that zero-duality-gap is achievable and the joint scheduling problem can be solved through a series of subproblems whose closed-form solutions are found. Moreover, for the scenario without subcarrier pairing we prove that the relaxation of allocation variables does not affect global optimality, i.e., even if the allocation variables are relaxed into continuous ones, binary variables are always retrievable as optimal solutions. Numerical examples are provided to corroborate the efficiency of the proposed approach.