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In this paper, the power control problem is considered for access-point based wireless networks under the SINR interference model. This problem is NP hard in terms of the number of APs in the network, and if not designed properly can have high polynomial complexity in terms of the power levels. We first separate the overall problem into two sub-problems using the primal-dual method. We then develop an efficient algorithm under the SINR-interference model that uses only two power levels to solve a subproblem of the overall power control problem, which we call the utility-independent power control (UIPC) subproblem. This approach allows the optimality gap of the UIPC subproblem to be bounded. Moreover, a two-stage iterative algorithm is developed that solves the overall power control problem within a small neighborhood of the global optimum. This offline algorithm has a significantly lower computational complexity than the globally optimal algorithm. Further, based on the structure of the iterative algorithm, an efficient heuristic two-stage greedy algorithm is proposed with low polynomial time complexity. Finally, numerical results are provided to demonstrate the efficacy of our solution.