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In this paper, the authors study the problem of client association, jointly with airtime sharing and contention resolution in a multi-cell WLAN with hidden terminals with the objective of achieving proportional fair download bandwidth allocation to the clients. They first formulate the problem as a utility maximization problem, which, due to the integral nature of association turns out to be a 0-1 (NP-hard) programming problem, then by studying its structure, they decompose it into two sub-problems: the client association problem on one hand, and the joint airtime sharing and contention resolution problem on the other.
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