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In an unstructured peer-to-peer (P2P) network (e.g., Gnutella), participating peers choose their neighbors randomly such that the resultant P2P network mismatches its underlying physical network, resulting in the lengthy communication between the peers and redundant network traffics generated in the underlying network. Previous solutions to the topology-mismatch problem in the literature are far from the optimum. In this paper, we propose a novel topology-matching algorithm based on the Metropolis-Hastings method. Through extensive simulations, we show that our proposal constructs an unstructured P2P network where a broadcast message, originated by any node v, reaches any other node u by taking approximately the only physical end-to-end delay between v and u.