To serve the peak trac demand, Wi-Fi networks that consist of a high-density access points (APs) have been deployed. Dense Wi-Fi networks incur two critical problems, energy waste and interference. In this paper, we solve these problems throughout optimized management of operation mode (on/of) of APs and user association according to traffic demand. We propose the rounding algorithm based on linear programming (LP) to minimize the average power consumption of APs while ensuring coverage of the active users and avoiding interference. We provide the theoretical performance guarantee of our algorithm in terms of approximation ratio and polynomial complexity. Moreover, in our simulations, the suggested algorithm shows near-optimal performance with very short run time. In other words, we suggest a promising solution even in practice as theory promises. To our best knowledge, we are the first to theoretically solve the energy eciency and interference problem in Wi-Fi networks at the same time.