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When streaming packetized media data over a lossy packet network, it is desirable to use transmission strategies that minimize the expected distortion subject to a constraint on the expected transmission rate. Because the computation of such optimal strategies is usually an intractable problem, fast heuristic techniques are often used. We first show that when the graph that gives the decoding dependencies between the data packets is reducible to a tree, optimal transmission strategies can be efficiently computed with dynamic programming algorithms. The proposed algorithms are much faster than other exact algorithms developed for arbitrary dependency graphs. They are slower than previous heuristic techniques but can provide much better solutions. We also show how to apply our algorithms to find high-quality approximate solutions when the dependency graph is not tree reducible. To validate our approach, we run simulations for MPEG1 and H.264 video data. We first consider a simulated packet erasure channel. Then we implement a real video streaming system and provide experimental results for an Internet connection.