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In this paper, we propose a fast and efficient adaptive transmission algorithm for the mobile WiMAX system. In our algorithm, we select the position of the boundary between the downlink and uplink subframes, the positions of the service flows within the frame, the coding and modulation schemes, and the transmission power values. Our algorithm gains high spectral efficiency, satisfies quality-of-service (QoS) requirements for the service flows, and has low computational complexity. The algorithm includes a frame boundary position optimization procedure, downlink and uplink optimization procedures, as well as a procedure that selects a transmission power value that enables satisfaction of the QoS requirements. All these procedures are novel, efficient, and fast. We evaluate the adaptive transmission algorithm by performing a system-level simulation of the mobile WiMAX system with multisector topology. We show that our algorithm has high spectral efficiency and low computational complexity, enabling QoS provisioning.