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The benefits of cognitive radio networking (CRN) have been well recognized with the emerging wireless applications in recent years. While many existing works assume that the secondary transmissions are negative interferences to the primary users (PUs), in this paper, we take secondary users (SUs) as positive potential cooperators for the PUs. In particular, we consider the problem of cooperative relay selection, in which the PUs actively select appropriate SUs as relay nodes to enhance their transmission performance. The most critical challenge for such a problem is how to select a relay efficiently. Due to the potentially large number of SUs, it is infeasible for a PU to first scan all the SUs and then pick the best. Basically, the PU transmitter intends to observe the SUs sequentially. After observing an SU, the PU needs to make a decision regarding whether to terminate its observation and use the current SU as its relay or to skip it and observe the next SU. We address this problem by using the optimal stopping theory and derive the optimal stopping rule. We also discuss the optimal observation order of the SUs and analyze the collision probability. To evaluate the performance of our proposed scheme, we compare our optimal stopping policy with the random selection policy through simulation study, and the results demonstrate the superiority of our policy. Extensive simulation study is conducted to investigate the impact of different parameters on the system performance, and the results indicate that our algorithm can satisfy different system requirements by carefully tuning the corresponding system parameters. [ABSTRACT FROM PUBLISHER]