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In this paper, the problem of allocating users to radio resources (i.e., subcarriers) in the downlink of an OFDMA cellular network is addressed. The authors consider a multi-cellular environment with a realistic interference model and a margin adaptive approach, i.e., they aim at minimizing total transmission power while maintaining a certain given rate for each user. The computational complexity issues of the resulting model is discussed and proving that the problem is NP-hard in the strong sense. Heuristic approaches, based on network flow models, that finds optima under suitable conditions, or "Reasonably good" solutions in the general case are presented.
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