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Optimization based spectrum sharing strategies have been widely studied. However, these strategies usually require a great amount of real-time computation and significant control delay, and thus are hard to be fulfilled in practical scenarios. This paper investigates optimal real-time spectrum sharing between a cooperative relay network (CRN) and a nearby ad hoc network. Specifically, we optimize the spectrum access and resource allocation strategies of the CRN so that the average traffic collision time between the two networks can be minimized while maintaining a required throughput for the CRN. The development is first for a frame-level setting, and then is extended to an ergodic setting. For the latter setting, we propose an appealing optimal real-time spectrum sharing strategy via Lagrangian dual optimization. The proposed method only involves a small amount of real-time computation and negligible control delay, and thus is suitable for practical implementations. Simulation results are presented to demonstrate the efficiency of the proposed strategies.