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In this letter, we propose joint relay selection and power allocation schemes for maximization of the throughput of an amplify-and-forward (AF) cooperative communication system where the source and the relays are energy harvesting (EH) nodes. We formulate an offline optimization problem which can be solved optimally by the generalized Bender's decomposition. For real-time implementation with low computational complexity, we propose two suboptimal online power allocation schemes. The performance of the proposed schemes is evaluated via simulations.