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A fast optimal algorithm for solving radio resource allocation (RRA) problems in orthogonal frequency division multiple access (OFDMA) systems is proposed based on branch- and-bound (BnB) approach. The proposed algorithm offers the same performance as that achieved by some other existing optimal algorithms but with much reduced average computational complexity. As an effort in providing trade-off between performance and computational complexity, two suboptimal algorithms are also developed. Simulation results are shown to compare the performance and complexity of the proposed suboptimal algorithms with several existing algorithms.