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Recently, there has been increasing interest in research on data sharing in peer-to-peer networks. In our previous work, we proposed a novel update propagation strategy that creates an n-ary tree, whose root is the owner of the original data while the other nodes are peers holding its replicas, and propagates the update information according to the tree. In this paper, we extend our previous strategy to further reduce the delay for update propagation and to tolerate peers' failure. To achieve this, in the extended strategy, peers participating in the tree record the information of their ancestors and children in the tree and reconstruct the tree using that information when some peers in the tree fail.