Faster construction of overlay networks

Abstract

We consider the problem of transforming any weakly connected overlay network of polylogarithmic degree into a topology of logarithmic diameter. The overlay network is modeled as a directed graph, in which messages are sent in synchronous rounds, and new edges can be established by sending node identifiers. However, every node can only send and receive a polylogarithmic number of bits in each round, which makes the naive approach of introducing all neighbors to each other until the network forms a clique infeasible. We present an algorithm that takes time O(log3/2 n),, w.h.p. At the heart of our algorithm lies a deterministic strategy to group and merge large components of nodes, but we make use of randomized load-balancing techniques to keep the communication load of each node low. To the best of our knowledge, this is the first algorithm to improve upon the algorithm by Angluin et al. [SPAA 2005], which solves the problem in time O(log3/2 n), and comes closer to the Ω(log n) lower bound.