### Abstract

Broadcasting is an information dissemination process in communication networks whereby a message, originated at any node of a network, is transmitted to all other nodes of the network. In c-broadcasting, each node having the message completes up to c transmissions to its neighbors over the communication lines in one time unit. In a k-fault tolerant c-broadcast network, the broadcasting process can be accomplished even if k communication lines fail. This paper presents innovative binary linear programming formulations to construct c-broadcast graphs, k-fault-tolerant c-broadcast graphs, and their time-relaxed versions. The proposed mathematical models are used to generate eight previously unknown minimum c-broadcast graphs, new upper bounds for eleven other instances of the c-broadcast problem, and over 30 minimum k-fault-tolerant c-broadcast graphs. The paper also provides a construction method to produce an upper bound for an infinite family of k-fault-tolerant c-broadcast graphs.

Original language | English (US) |
---|---|

Pages (from-to) | 173-184 |

Number of pages | 12 |

Journal | Discrete Applied Mathematics |

Volume | 204 |

DOIs | |

State | Published - May 11 2016 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete Applied Mathematics*,

*204*, 173-184. https://doi.org/10.1016/j.dam.2015.11.008

}

*Discrete Applied Mathematics*, vol. 204, pp. 173-184. https://doi.org/10.1016/j.dam.2015.11.008

**Binary linear programming models for robust broadcasting in communication networks.** / McGarvey, Ronald G.; Rieksts, Brian Q.; Ventura, José A.; Ahn, Namsu.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Binary linear programming models for robust broadcasting in communication networks

AU - McGarvey, Ronald G.

AU - Rieksts, Brian Q.

AU - Ventura, José A.

AU - Ahn, Namsu

PY - 2016/5/11

Y1 - 2016/5/11

N2 - Broadcasting is an information dissemination process in communication networks whereby a message, originated at any node of a network, is transmitted to all other nodes of the network. In c-broadcasting, each node having the message completes up to c transmissions to its neighbors over the communication lines in one time unit. In a k-fault tolerant c-broadcast network, the broadcasting process can be accomplished even if k communication lines fail. This paper presents innovative binary linear programming formulations to construct c-broadcast graphs, k-fault-tolerant c-broadcast graphs, and their time-relaxed versions. The proposed mathematical models are used to generate eight previously unknown minimum c-broadcast graphs, new upper bounds for eleven other instances of the c-broadcast problem, and over 30 minimum k-fault-tolerant c-broadcast graphs. The paper also provides a construction method to produce an upper bound for an infinite family of k-fault-tolerant c-broadcast graphs.

AB - Broadcasting is an information dissemination process in communication networks whereby a message, originated at any node of a network, is transmitted to all other nodes of the network. In c-broadcasting, each node having the message completes up to c transmissions to its neighbors over the communication lines in one time unit. In a k-fault tolerant c-broadcast network, the broadcasting process can be accomplished even if k communication lines fail. This paper presents innovative binary linear programming formulations to construct c-broadcast graphs, k-fault-tolerant c-broadcast graphs, and their time-relaxed versions. The proposed mathematical models are used to generate eight previously unknown minimum c-broadcast graphs, new upper bounds for eleven other instances of the c-broadcast problem, and over 30 minimum k-fault-tolerant c-broadcast graphs. The paper also provides a construction method to produce an upper bound for an infinite family of k-fault-tolerant c-broadcast graphs.

UR - http://www.scopus.com/inward/record.url?scp=84949640401&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84949640401&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2015.11.008

DO - 10.1016/j.dam.2015.11.008

M3 - Article

AN - SCOPUS:84949640401

VL - 204

SP - 173

EP - 184

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -