Distributed Resource Discovery in Sub-Logarithmic Time

We present a new distributed algorithm for the resource discovery problem introduced by Harchol-Balter, Leighton, and Levin in PODC'99. The resource discovery problem consists of a synchronous network with n machines in which at any timestep any machine v can PUSH or PULL a message to/from any other machine u whose (IP) address is known to v. Messages can contain addresses which then change the "topology". The goal of a distributed resource discovery problem is to enable all machines to learn the addresses of all other machines as fast as possible while keeping the number of messages sent low. We present a randomized distributed algorithm that achieves this goal in O(log D log log n) rounds using O(n) messages, where D is the strong diameter of the initial topology. Up to the log log n factor, our round complexity is best possible given the trivial Omega(log D) lower bound. For many typical networks with D = o(n), our running time is a drastic improvement over prior O(log n) round algorithms. In particular, for networks with polylogarithmic diameter an O(log(2) log n) running time and thus an almost exponential speedup is obtained.