Beyond the Lower Bound: A Unified and Optimal P2P Construction Method

The topological properties of overlay networks are critical for the performance of peer-to-peer (P2P) systems. The size of routing table and the diameter are among the most important parameters which measure the autonomy, efficiency, robustness and load balancing of P2Ps, and the Moore bound sets the optimal tradeoff between diameter and degree for any graph. In order to improve the four features for structured P2P networks, researchers have proposed many designs based on the interconnect networks which can approximately achieve the Moore bound. However, the performances of these systems in dynamic environments are far worse than their corresponding interconnect networks in the static environment. Moore bound cannot give a good description for existing P2P systems due to their dynamic features. In this study, therefore, we first prove a new lower bound of the network diameter and average query distance in a highly dynamic environment. The routing latency of the existing systems cannot be more better than the new bound. This is because the existing systems require a fixed number of peers known a priori. P2P systems on the other hand, typically are dynamic, meaning that peers frequently join or leave. To solve the issue, we propose a dynamic multi-way trie tree structure, based on which any interconnect network can be adopted to construct a P2P system. The unified construction method also consists of a series of optimal schemes for P2P systems. DeBruijn and butterfly representing the single and hybrid protocols based on the dynamic multi-way trie tree structure are used to construct two new P2P systems (DPhoenix, BPhoenix) whose performances can exceed the new bound. Also, DPhoenix and BPhoenix can be easily applied to other interconnection networks after minimal modifications, such as, hypercube, kautz, shuffle-exchange and CCC.