## Abstract

We consider all-cast 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.

Original language | English (US) |
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Article number | 6482634 |

Pages (from-to) | 5075-5087 |

Number of pages | 13 |

Journal | IEEE Transactions on Information Theory |

Volume | 59 |

Issue number | 8 |

DOIs | |

State | Published - 2013 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Information Systems
- Computer Science Applications
- Library and Information Sciences

## Keywords

- All-cast
- Erdöcs-Rényi random graph
- Steiner tree
- broadcast
- flows
- matching
- multicast
- network coding
- random graph
- tree packing