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In this paper we consider resource allocation for an OFDMA-based cognitive radio point-to-multipoint network with fixed users. Specifically, we assume that secondary users are allowed to transmit on any subchannel provided that the interference that is created to any primary users is below a critical threshold. We focus on the downlink. We formulate the joint subchannel, power and rate allocation problem in the context of finite queue backlogs with a total power constraint at the base station. Thus, users with small backlogs are only allocated sufficient resources to support their backlogs while users with large backlogs share the remaining resources in a fair and efficient fashion. Specifically, we formulate the problem as a max-min problem that is queue-aware, i.e., on a frame basis. We maximize the smallest rate of any user whose backlog cannot be fully transmitted. While the problem is a large non-linear integer program, we propose an iterative method that can solve it exactly as a sequence of linear integer programs, which provides a benchmark against which to compare fast heuristics. We consider two classes of heuristics. The first is an adaptation of a class of multi-step heuristics that decouples the power and rate allocation problem from the subchannel allocation and is commonly found in the literature. To make this class of heuristics more efficient we propose an additional (final) step. The second is a novel approach, called selective greedy, that does not perform any decoupling. We find that while the multi-step heuristic does well in the non-cognitive setting, this is not always the case in the cognitive setting and the second heuristic shows significant improvement at reduced complexity compared to the multi-step approach. Finally, we also study the influence of system parameters such as number of primary users and critical interference threshold on secondary network performance and provide some valuable insights on the operation of such systems.