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One of the most appealing characteristics of unstructured P2P overlays is their enhanced self-* properties, which results from their loose, random structure. In addition, most of the algorithms which make searching in unstructured P2P systems scalable, such as dynamic querying and 1-hop replication, rely on the random nature of the overlay to function efficiently. The underlying communications network (i.e., the Internet), however, is not as randomly constructed. This leads to a mismatch between the distance of two peers on the overlay and the hosts they reside on at the IP layer, which in turn leads to its misuse. The crux of the problem arises from the fact that any effort to provide a better match between the overlay and the IP layer will inevitably lead to a reduction in the random structure of the P2P overlay, with many adverse results. With this in mind, we propose ITA, an algorithm which creates a random overlay of …