Neighbor Table Construction and Update for Resilient Hypercube Routing in P 2 P Networks

Several proposed peer-to-peer networks use hypercube rou ting for scalability. Consistency of neighbor tables in hypercube routing guarantees the existence of a path from any source node to any destination node. Such consistency, however, can be broken by node failu res. To improve the robustness of hypercube routing, we first generali ze the concept of consistencyto K-consistency , for K ≥ 1, which is shown to provide at leastK disjoint paths for any source-destination pair with a probability close to 1. Our next objective is to design and specify a new jo in protocol together with a proof that it generatesK-consistent neighbor tables for an arbitrary number of concurrent joins. We first present a conceptual foundation, called C-set trees , for protocol design and reasoning aboutKconsistency. We then present a detailed specification of a jo in protocol, and a rigorous proof of correctness for the join protocol. The crux of our proof is based upon induction on C-set trees. Both theoretical ana lysis and simulation results show that the join protocol is scalable to a l arge number of network nodes. Keywords—Peer-to-peer networks, consistency, K-consistency, hypercube routing, join protocol, protocol design and verification, C-set tree