Achieving the Optimal Steaming Capacity and Delay Using Random Regular Digraphs in P2P Networks

Abstract: In earlier work, we showed that it is possible to achieve $O(\log N)$ streaming delay with high probability in a peer-to-peer network, where each peer has as little as four neighbors, while achieving any arbitrary fraction of the maximum possible streaming rate. However, the constant in the $O(log N)$ delay term becomes rather large as we get closer to the maximum streaming rate. In this paper, we design an alternative pairing and chunk dissemination algorithm that allows us to transmit at the maximum streaming rate while ensuring that all, but a negligible fraction of the peers, receive the data stream with $O(\log N)$ delay with high probability. The result is established by examining the properties of graph formed by the union of two or more random 1-regular digraphs, i.e., directed graphs in which each node has an incoming and an outgoing node degree both equal to one.