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This paper presents a distortion optimized streaming algorithm for on-demand streaming of multimedia. Given the pre-encoded packets of a multimedia stream, we propose a fast algorithm for selecting an appropriate subset of these packets such that the overall client distortion is minimized. This minimization is performed within the rate constraints imposed by the communication channel. In particular, at each transmission opportunity, the proposed approach uses a linear-time algorithm to select the best packet to transmit through the minimization of the expected client distortion. The time complexity of the algorithm is reduced through a factorization of the streaming policy into simpler terms and performing a greedy optimization to select the packet. Inevitably, this in itself leads to sub-optimal results. To alleviate the adverse impact of the greedy optimization, the cost function is penalized with the expected buffer occupancy at the end of the epoch of the optimization. We pose this problem as a Lagrangian minimization. We demonstrate the efficacy of the proposed approach through empirical evaluation.