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The paper addresses the distributed path computation and rate allocation problems for video delivery over multipath networks. The streaming rate on each path is determined such that the end-to-end media distortion is minimized, when a media client aggregates packets received via multiple network channels to the streaming server. In common practical scenarios, it is, however, difficult for the server to have the full knowledge about the network status. Therefore, we propose here a distributed path selection and rate allocation algorithm, where the network nodes participate to the optimized path selection and rate allocation based on their local view of the network. This eliminates the need for end-to-end network monitoring, and permits the deployment of large scale rate allocation solutions. We design a distributed algorithm for optimized rate allocation, where the media client iteratively determines the best set of streaming paths, based on information gathered by network nodes. Each intermediate node then forwards incoming media flows on the outgoing paths, in a distributed manner. The proposed algorithm is shown to quickly converge to the rate allocation that provides a maximal quality to the video client. We also propose a distributed greedy algorithm that achieves close-to-optimal end-to-end distortion performance in a single pass. Both algorithms are shown to outperform simple heuristic-based rate allocation approaches for numerous random network topologies. They offer an interesting solution for media-specific rate allocation over large scale multipath networks.