Optimal Serial Broadcast of Successive Chunks

Abstract

This paper studies the problem of broadcasting successive chunks to all nodes in a network under an assumption such that each node can upload a chunk to exactly one node at a time. This models the delivery of a video stream in a Peer-to-Peer (P2P) network in which chunks of a stream are successively given by the media server. We propose two schemes for solving the problem. The first scheme attains an optimum broadcast time of $\lceil{\lg n}\rceil$ steps, where n is the number of nodes, using an overlay network in which each node has $\mathcal{O}(\lg^2 n)$ children. The second scheme reduces the number of children by slightly increasing the broadcast time. More concretely, it completes each broadcast in $\lg n+o(\lg n)$ steps when the number of children is bounded by O((f(n))²) for any function satisfying f(n) = ω(1) and f(n) = o(n).