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Media streaming is an important Internet application and has received more and more attention in recent years. Traditional media streaming systems are deployed in a server-client mode which scales poorly with the increasing population of the clients. Peer-to-peer media streaming can greatly enhance the scalability of the system by employing the clients to help forward the media content. In this paper, we consider optimizing the overlay construction for peer-to-peer streaming systems with heterogeneous access link bandwidths. Our goal is to maximize the total downloading rate and satisfy the heterogeneous downloading requirements when the uplink bandwidth is limited. We first formalize it into a problem of finding maximum number of edge disjoint trees in a graph which models the peers and their access link bandwidths. Then we give a centralized heuristic algorithm to solve the problem. Based on the centralized algorithm, we further propose a distributed algorithm which constructs an adaptive overlay topology that can adapt itself to the changing peers such that the end-to-end delay and link stress are minimized. We compare our scheme with another recently proposed scheme called MDM through simulations. Our simulation results show that the proposed scheme outperforms MDM by about 30% with respect to the average peer satisfaction. In addition, the proposed scheme achieves less link stress than MDM.