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Network power minimization problem is considered for orthogonal frequency-division multiple access (OFDMA) relay systems. To devise a simple algorithm, we introduce a new cost that is an inverse-of-required-minimum power for a target rate. Using the new cost, we propose a greedy-search-based subchannel resource allocation algorithm with a communication mode selection and relay processing adaptation. The communication mode selection allows each user to employ multiple (hybrid) modes with direct, amplify-and-forward (AF), and decode-and-forward (DF) communications, and the relay processing adaptation controls relay transmit power, so that network power consumption can be significantly reduced as verified in simulation.