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For the mobile users (MUs) installed with IEEE 802.11 wireless adapters, the default best-signal-strength-based access point (AP) selection is limited since it does not consider fairness and multi-rate issues. In this paper, we propose a distributed AP selection algorithm for newly joining MU and already associated MUs to be adaptive to their joining order and the dynamic wireless environment. We also prove the stability of proposed algorithm and analyze its complexity. Finally, with extensive evaluations, we show that proposed scheme can greatly improve the fairness without significantly sacrificing the efficiency.