### 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) |
---|---|

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 - Jul 29 2013 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*IEEE Transactions on Information Theory*,

*59*(8), 5075-5087. [6482634]. https://doi.org/10.1109/TIT.2013.2253543

**An asymptotically optimal push-pull method for multicasting over a random network.** / Swamy, Vasuki Narasimha; Bhashyam, Srikrishna; Sundaresan, Rajesh; Viswanath, Pramod.

Research output: Contribution to journal › Article

*IEEE Transactions on Information Theory*, vol. 59, no. 8, 6482634, pp. 5075-5087. https://doi.org/10.1109/TIT.2013.2253543

}

TY - JOUR

T1 - An asymptotically optimal push-pull method for multicasting over a random network

AU - Swamy, Vasuki Narasimha

AU - Bhashyam, Srikrishna

AU - Sundaresan, Rajesh

AU - Viswanath, Pramod

PY - 2013/7/29

Y1 - 2013/7/29

N2 - 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.

AB - 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.

KW - All-cast

KW - Erdöcs-Rényi random graph

KW - Steiner tree

KW - broadcast

KW - flows

KW - matching

KW - multicast

KW - network coding

KW - random graph

KW - tree packing

UR - http://www.scopus.com/inward/record.url?scp=84880515359&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880515359&partnerID=8YFLogxK

U2 - 10.1109/TIT.2013.2253543

DO - 10.1109/TIT.2013.2253543

M3 - Article

AN - SCOPUS:84880515359

VL - 59

SP - 5075

EP - 5087

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 8

M1 - 6482634

ER -