A peer-to-peer protocol in hierarchical navigable small-world network

We improve Kleinberg's hierarchical small world network model ^[1] to implement a peer-to-peer overlay network. In the overlay, all the nodes are treated as leaves which are uniformly distributed in a complete 2-ary tree, and the distance between nodes is defined as the height of their lowest common ancestor in the tree. Every node in the overlay is linked to at least one d-distance node if the d-distance nodes exist. Through simulation ^[2], we demonstrate that, the overlay has average (log2N)/2 routing hops, a 100% routing success rate, while the average node degree is log2N , the number of messages for node joining is (log2N)/2, the number of message for node leaving is log2N.