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In a peer-to-peer overlay network, the phenomenon of multiple overlay links sharing bottleneck physical links leads to correlation of overlay link capacities. We are able to more accurately model the overlay by incorporating these linear capacity constraints (LCCs). We formulate the problem of maximizing bandwidth in overlay multicast using our LCC model. We show that finding a maximum bandwidth multicast tree in an overlay network with LCC is NP-complete. Therefore, an efficient heuristics algorithm is designed to solve the problem. Extensive simulations show that our algorithm is able to construct multicast trees that are optimal or extremely close to optimal, with significantly higher bandwidth than trees formed in overlays with no LCC. Furthermore, we develop a fully distributed algorithm for obtaining near-optimal multicast trees, by means of gossip-based algorithms and a restricted but inherently distributed class of LCC (node-based LCC). We demonstrate that the distributed algorithm converges quickly to the centralized optimal and is highly scalable.