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Orthogonal Frequency Division Multiplexing (OFDM) has become the de facto standard for fourth generation wireless networks. In such a network, the frequency band is divided into numerous orthogonal sub-carriers. In each time-slot, disjoint sets of sub-carriers can be assigned to users based on some target objective. The users in turn transmit data by spreading the information across the assigned sub-carriers. The main contribution of this work is a formal analysis of the complexity of this class of resource allocation problems for various objectives and scenarios. Specifically the authors formally prove that the sub-carrier resource allocation problem is NP-hard for both power minimization as well as rate maximization in both uplink and downlink scenarios.
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