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In this paper, we present DKS (N, k, f), a family ofinfrastructures for building Peer-To-Peer applications.Each instance of DKS (N, k, f) is a fully decentralizedoverlay network characterized by three parameters: Nthe maximum number of nodes that can be in the network; k the search arity within the network and f thedegree of fault-tolerance. Once these parameters are instantiated, the resulting network has several desirableproperties. The first property, which is the main contribution of this paper, is that there is no separate procedurefor maintaining routing tables; instead, any out-of-dateor erroneous routing entry is eventually corrected on-the-fly thereby, eliminating unnecessary bandwidth consumption. The second property is that each lookup request is resolved in at most logk(N) overlay hops under normal operations. Third, each node maintains only(k - 1)logk(N) + 1 addresses of other nodes for routingpurposes.Fourth, new nodes can join and existingnodes can leave at will with a negligible disturbance tothe ability to resolve lookups in logk(N) hops in average.Fifth, any pair key/value that is inserted into the systemis guaranteed to be located even in the presence ofconcurrent joins.Sixth, even if f consecutive nodes failsimultaneously, correct lookup is still guaranteed.