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The blind flooding algorithm under a time-to-live (TTL) constraint used in unstructured peer-to-peer (P2P) networks, such as Gnutella, may cause a large amount of network traffic. The algorithm cannot guarantee for acquiring the required data objects, especially for rare ones. To mitigate these problems, this paper proposes PercolationNET, a multi-tree sub-overlay, which is built on top of an existing P2P overlay (named original overlay). PercolationNET organizes peers in a tree-based structure which facilitates reliable and efficient message dissemination for search. The search process is divided into two stages. A query message is first propagated on the original overlay, and then broadcast along the sub-overlay PercolationNET. PercolationNET combines the advantages of fast coverage speed in flooding-based scheme and low traffic cost in tree-based scheme. The experimental results of PercolationNET compared with FloodNet confirm the superiority of PercolationNET in achieving faster coverage speed and lower message cost.