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The traffic load of wireless LANs is often unevenly distributed among the access points (APs), which results in unfair bandwidth allocation among users. We argue that the load imbalance and consequent unfair bandwidth allocation can be greatly reduced by intelligent association control. In this paper, we present an efficient solution to determine the user-AP associations for max-min fair bandwidth allocation. We show the strong correlation between fairness and load balancing, which enables us to use load balancing techniques for obtaining optimal max-min fair bandwidth allocation. As this problem is NP-hard, we devise algorithms that achieve constant-factor approximation. In our algorithms, we first compute a fractional association solution, in which users can be associated with multiple APs simultaneously. This solution guarantees the fairest bandwidth allocation in terms of max-min fairness. Then, by utilizing a rounding method, we obtain the integral solution from the fractional solution. We also consider time fairness and present a polynomial-time algorithm for optimal integral solution. We further extend our schemes for the on-line case where users may join and leave dynamically. Our simulations demonstrate that the proposed algorithms achieve close to optimal load balancing (i.e., max-min fairness) and they outperform commonly used heuristics.