Distributed construction of random expander networks

A novel distributed algorithm for constructing random overlay networks that are composed of d Hamilton cycles is presented. The protocol is completely decentralized as no globally-known server is required. The constructed topologies are expanders with O(log/sub d/ n) diameter with high probability. Our construction is highly scalable because both the processing and the space requirements at each node grow logarithmically with the network size. A new node can join the network in O(log/sub d/ n) time with O(d log/sub d/ n) messages. A node can leave in O(1) time with O(d) messages. The protocol is robust against an offline adversary selecting the sequence of the join and leave operations. We also discuss a layered construction of the random expander networks in which any node can be located in O(log n) time. The random expander networks have applications in community discovery, distributed lookup service, and dynamic connectivity.