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Current peer-to-peer lookup algorithms have been designed with the assumption that routing information at each member node must be kept small, so that the bookkeeping required to respond to system membership changes is also small. In this paper, we show that this assumption is unnecessary, and present a technique that maintains complete routing tables at each node. The technique is able to handle frequent membership changes and scales to large systems having more than a million nodes. The resulting peer-to-peer system is robust and can route lookup queries in just one hop, thus enabling applications that cannot tolerate the delay of multi-hop routing.