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Cognitive radio has received great attention recently for its ability to improve spectrum efficiency by letting secondary users to access spectrum resource that is unoccupied by primary users. However, cognitive radio also brings new challenges in the design of future wireless networks. In this paper, we investigate the problem of resource allocation in cognitive radio networks. Specifically, we consider the problem of proportional fair scheduling in cognitive radio relay networks. Our problem formulation takes into account the fluctuations of usable spectrum resource, channel quality variations caused by frequency selectivity, and interference caused by different transmit power levels. We prove that the problem is NP-hard and is computationally infeasible to be solved in a timely manner by using brute force algorithms. An easy-to-compute upper bound for the formulated problem is also derived. We then propose two heuristic algorithms that are easy-to-implement, yet achieve performance close to the upper bound. The proposed algorithms can be executed and finished within 1 millisecond. Thus, they can meet the requirement of real-time scheduling. Simulation experiments verify that the proposed algorithms can achieve good proportional fairness among users and enhance system throughput by proper power control.