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The resource allocation problem of minimising transmission power with per user rate constraint is studied for energy efficiency of multiuser multicarrier systems. The authors introduce an algorithm that deploys a flow-based decomposition strategy, called the network-flow-based algorithm (NFBA), to circumvent the NP-hard complexity of the resource allocation problem. The authors prove global optimality of the algorithm for the case of a flat-fading channel. For the general frequency selective channel, the flow size is adjusted adaptively to minimise the transmission power. Also, a compact integer programming formulation is developed to provide tight lower and upper bounds of the minimum power. Numerical results show that the authors' proposed NFBA achieves near-optimal performance with polynomial complexity even for large-scale systems.