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Peer-to-Peer (P2P) video streaming services on the Internet have gained increasing popularity during the past few years. However, many problems still need to be addressed before it can be widely deployed in the wireless environment. The existing P2P overlay network architecture hides the underlying network topology, assuming channel quality is always in perfect condition. This works well for the Internet-based services, but hardly meets the user-perceived video quality requirement in wireless environments due to the time-varying nature of wireless channels. Inspired by the tightly-coupled relationship between P2P overlay networks and the underlying networks, we propose a novel scheduling algorithm on the basis of a quality-driven cross-layer design framework to jointly optimize the parameters of different network layers to achieve highly- improved video quality for P2P video streaming applications in multi-hop wireless mesh networks. In this paper, the quality-driven P2P scheduling algorithm is formulated into a distributed distortion-delay optimization problem, where the expected video distortion is minimized under the constraint of a given packet playback deadline to select the optimal combination of system parameters residing in different network layers. Then we provide the algorithmic solution to the formulated problem based on dynamic programming. The distributed optimization running on each partner node adopted in the scheduling algorithm greatly reduces the computational intensity. Extensive experimental results demonstrate 5-15dB quality enhancement in terms of PSNR by using the proposed scheduling algorithm.