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Relay selection is a challenging issue in cooperative communication networks. In particular, in a multi-user multi- concurrent-transmission network, effects of the resource sharing of a relay by its served users on the relay selection strategy need to be taken into account. There is little research on this investigation in literature. In this paper, we propose a novel efficient and fair relay selection strategy, in which individual user's QoS requirement is inherently taken into account. In terms of efficiency, the proposed strategy is of low computational complexity. In terms of fairness, the system resource is utilized fairly among all relaying nodes so that the system has the best potential to accommodate as many users as possible. Simulation results indicate that the proposed selection strategy outperforms many existing ones, therefore justifying our arguments.