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Summary form only given. Power control is an important issue in wireless networks, which still has no satisfactory solution. Due to the limited amount of power available to wireless units, there is a need for systems that operate with reduced power consumption levels. We propose a new model for the problem, that exploits the relationship among necessary power and reach of broadcast. The resulting model is called the power control problem in ad hoc networks (PCADHOC). We derive a linear integer programming model, which is used to find lower bounds on the amount of required power. The constraints of the problem guarantee that all required transmissions can be successfully performed. A distributed algorithm based on variable neighborhood search is proposed to solve the PCADHOC. The results of experiments with the algorithm show that the power savings are considerable.