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This paper addresses the problem of allocating spatially reused frequency channels in ad hoc networks to satisfy data rate constraints on various links. The data rate requirement of each link is satisfied by using adaptive modulation. Power control is used to maintain the required signal to interference and noise ratio (SINR) in the presence of interference, which is caused due to frequency reuse. The objective is to minimize the total transmitted power over the entire network while satisfying the data rate requirement of each link. We show that this problem is a hard optimization problem and present a heuristic algorithm. The simulation results show that our algorithm results in an efficient assignment of frequencies and transmitter power levels in terms of the energy required for transmitting each bit of information. The results also demonstrate that our algorithm outperforms existing techniques.