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The problem of resource allocation for multiuser OFDM based cognitive network is studied. A new greedy algorithm based on minimum remaining constraint space (MRCS) is proposed to allocate subcarrier, power and bit efficiently. Both active frequency bands occupied by primary users and spectrum holes can be used by cognitive users, as long as the interferences introduced by cognitive users to primary users below a certain threshold. Simulation results show that the proposed algorithm is fit for the practical environment and has better performance than other existing allocation algorithms.