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In a multihomed video streaming system, a video sequence is simultaneously transmitted over multiple access networks to a client. In this paper, we formulate the rate control and stream adaptation problems into a unified optimization problem, which determines the sending rates of individual networks, selects which video packets to transmit, and assigns each packet to an access network. We propose two heuristic algorithms with a trade-off between optimality and computational complexity. One of the proposed algorithms runs faster, while the other one results in better video quality. We propose a hybrid algorithm that demonstrates a good balance between optimality and computational complexity. We conduct extensive packet-level simulations to evaluate our algorithms using real network conditions and actual scalable video streams. We compare our algorithms against the rate control algorithms defined in the Datagram Congestion Control Protocol (DCCP) standard. The simulation results show that our algorithms significantly outperform current systems while being TCP-friendly. Our algorithms achieve at least 10 dB quality improvement over DCCP and result in up to 83% packet delivery delay reduction.