An asymptotically optimal push-pull method for multicasting over a random network

TL;DR

This paper analyzes the capacity of large random networks for multicasting and introduces a decentralized push-pull algorithm that asymptotically achieves optimal throughput without network coding.

Contribution

It provides an asymptotic analysis of the capacity region for multicast in random networks and proposes a novel decentralized push-pull method that attains optimal rates.

Findings

Normalized sum rate converges to a constant almost surely as network size grows.

The push-pull algorithm asymptotically achieves the capacity without network coding.

The study extends understanding of multicast capacity in large random networks.

Abstract

We consider allcast and multicast flow problems where either all of the nodes or only a subset of the nodes may be in session. Traffic from each node in the session has to be sent to every other node in the session. If the session does not consist of all the nodes, the remaining nodes act as relays. The nodes are connected by undirected links whose capacities are independent and identically distributed random variables. We study the asymptotics of the capacity region (with network coding) in the limit of a large number of nodes, and show that the normalized sum rate converges to a constant almost surely. We then provide a decentralized push-pull algorithm that asymptotically achieves this normalized sum rate without network coding.