Achieving Absolutely Optimal Block Pipelining in Organized Network Coded Gossip

We use random linear network coding with simple connection topology control to approach the theoretical limit on finish time of disseminating k blocks in a server cluster of n nodes. Unlike existing gossip schemes which rely on completely random contact, we prove that with random linear network coding, any receiver selection following a simple permutation rule can achieve a broadcast finish time of k + n and that a time-varying random permutation topology achieves a finish time of k + o (k) + O (log n), both with high probability. Since the theoretical limit on finish time is k + log2 n, our simple permutation algorithms achieve absolutely optimal (not only order-optimal) block pipelining for k blocks. Our results hold for both one-to-all (broadcast) and all-to-all transfers. We demonstrate the usefulness of the proposed organized network coded gossip with an application to content distribution in cluster computing systems like MapReduce.