Several peer-to-peer networks are based upon randomized graph topologies that permit e#cient greedy routing, e.g., randomized hypercubes, randomized Chord, skip-graphs and constructions based upon small-world percolation networks. In each of these networks, a node has out-degree #(log n), where n denotes the total number of nodes, and greedy routing is known to take O(log n) hops on average. We establish lower-bounds for greedy routing for these networks, and analyze Neighbor-of-Neighbor (NoN)-greedy routing. The idea behind NoN, as the name suggests, is to take a neighbor's neighbors into account for making better routing decisions.
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