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In this paper, cognitive radio wireless networks are investigated, in which a number of primary users (PUs) transmit in orthogonal frequency bands, and a number of secondary users (SUs) monitor the transmission status of the PUs and search for transmission opportunities in these frequency bands by collaborative detection. A network management problem is formulated to find the configuration of SUs (assignment of SUs) to detect PUs so that the best overall network performance is achieved. Two performance metrics are considered, both of which characterize the probability of errors for detecting transmission status of all PUs. For both metrics, a graphical representation of the problem is provided, which facilitates to connect the problems under study to the sum-product inference problem studied in probabilistic graphical models. Based on the elimination algorithm that solves the sum-product problem, a message passing algorithm is proposed to solve the problem under study in a computationally efficient manner and in a distributed fashion. The complexity of the algorithm is shown to be significantly lower than that of the exhaustive search approach. Moreover, a clique-tree algorithm is applied to efficiently compute the impacts of each SU's choice on the overall system performance. Finally, simulation results are provided to demonstrate the considerable performance enhancement achieved by implementing an optimal assignment of SUs.