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We consider small world graphs as defined by Kleinberg (2000), i.e., graphs obtained from a d-dimensional mesh by adding links chosen at random according to the d-harmonic distribution. This model aims at giving formal support to the "six degrees of separation" between individuals experienced by Milgram (1967),and verified recently by Dodds, Muhamad, and Watts (2003). In particular, Kleinberg shows that greedy routing performs in O(log2n) expected number of steps in d-dimensional augmented meshes, with O(log2n) bits of topological awareness per node, for any constant d ≥ 1. We show that giving O(log2n) bits of topological awareness per node decreases the expected number of steps of greedy routing to O(log1+1/dn) in d-dimensional augmented meshes. We also show that, independently of the amount of topological awareness given to the nodes, greedy routing performs in Ω(log1+1/dn) expected number of steps. In particular, augmenting the topological awareness above this optimum of O(log2n) bits would drastically decrease the performances of greedy routing. Moreover, our model demonstrates that the efficiency of greedy routing is sensible to the "world's dimension", in the sense that high dimensional worlds enjoy faster greedy routing than low dimensional ones. This could not be observed in Kleinberg's model. In addition to bringing new light to Milgram's experiment, our protocol presents several desirable properties. In particular, it is totally oblivious i.e., there is no header modification along the path from the source to the target, and the routing decision depends only on the target, and on information stored locally at each node. Finally, our protocol can obviously be used for the design of DHTs, in the same spirit as Symphony (2003).