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Optimal power allocation for multi-user amplify- and-forward wireless relay networks in which multiple source-destination pairs are assisted by a set of relays is investigated. Two relay power allocation strategies based on maximization of either i) the minimum rate among all users or ii) the weighted sum of rates are developed. A distributed implementation of the maximum weighted-sum-rate power allocation strategy is also studied. Numerical results demonstrate the efficiency of the proposed strategies and reveal their interesting throughput-fairness tradeoff in resource allocation.