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We develop a distributed throughput-optimal power allocation algorithm in wireless networks. The study of this problem has been limited due to the nonconvexity of the underlying optimization problems that prohibits an efficient solution even in a centralized setting. By generalizing the randomization framework originally proposed for input queued switches to SINR rate-based interference model, we characterize the throughput-optimality conditions that enable efficient and distributed implementation. Using gossiping algorithm, we develop a distributed power allocation algorithm that satisfies the optimality conditions, thereby achieving (nearly) 100 percent throughput. We illustrate the performance of our power allocation solution through numerical simulation.