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In 3G data networks, network operators would like to balance system throughput while serving users in a fair manner. This is achieved using the notion of proportional fairness. However, so far, proportional fairness has been applied at each base station independently. Such an approach can result in non-Pareto optimal bandwidth allocation when considering the network as a whole. Therefore, it is important to consider proportional fairness in a network-wide context with user associations to base stations governed by optimizing a generalized proportional fairness objective. This paper takes the first step in formulating and studying this problem rigorously. It shows that the general problem is NP-hard and it is also hard to obtain a close-to-optimal solution.

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