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This paper addresses aspects of routing strategy of a cellular network enhanced with two-hop fixed relay nodes. The routing strategy for each user is important design parameter because the terminal is energy-limited. To enhance the radio resource utility, a utility maximization framework via pricing is adopted for multi-cell distributed power allocation. Under the optimization physical layer transmission strategy, an efficient power-based routing algorithm is proposed in reverse link which selects the best route in the tradeoff between power consumption and data rate. It is demonstrated through intensive system-level simulation that the performance of our proposed routing algorithm is superior to several known routing algorithms.